i I rented a car [preterite]
ii I have rented a car [present perfect]
This question is about when to use the preterite, also called the simple past tense, versus the present perfect tense.
Unfortunately, there is no one simple rule when to use i as opposed to ii; the situation is a bit complicated.
CGEL says (in agreement with traditional grammar, for once) that there are four possible contexts in which the present perfect is justified. These are often referred to as 'types' of perfect, although that is a bit of a misnomer, because the syntactic construction is the same for all of them. These are the continuative perfect, the experiential/existential perfect, the resultative perfect, and the perfect of recent past.
In your example, there is not enough context to decide which of these applies; in principle, all four could. To see how that could happen, we add some disambiguating information (in boldface):
 i I have rented a car ever since. [continuative]
ii I have rented a car before. [experiential/existential]
iii I have rented a car, so I will be able to travel easily. [resultative]
iv I have just rented a car. [recent past]
Both the preterite and the present perfect relate two time domains as one anterior to (i.e. before) the other. The one that's further in the past is called the 'time referred to', Tr. The other is called the 'time of orientation', TO. TO sometimes coincides with 'now' (in which case we say it is 'interpreted deictically'), but sometimes not; all we can say about TO in general is that it is 'the time relative to which the speaker asserts Tr to be in the past'. With the preterite, Tr is strictly in the past of TO. But with the present perfect, while Tr certainly begins in the past, it is possible for it to extend all the way to TO. When that happens, we have a continuative reading of the present perfect; othewise we have a non-continuative reading.
(Another difference between the two tenses concerns how they interpret TO. In the preterite, TO is normally interpreted deictically, i.e. TO is normally 'now', the 'time of utterance'. In the case of the perfect, the location of TO itself is not interpreted deictically by default, and so its location relative to 'now' is more easily movable than in the case of the preterite.)
The preterite vs the continuative perfect
Note that there can be no confusion between the preterite and the present perfect in the continuative reading. Compare (CGEL, p. 141)
 NON-CONTINUATIVE CONTINUATIVE
(Tr wholly before TO) (Tr before and up to TO)
i a. He may have told her last week. b. He may have been here ever since.
ii a. He told her last week. b. *He was here ever since.
[The continuative reading] is illustrated in [ib], where his being here covers a period beginning in the past and extending up to now. The deviance of [iib] shows that the preterite cannot be used for this meaning—only for the non-continuative reading where Tr is wholly before TO, as in the [a] examples.
The temporal relation "Tr wholly before or before and up to TO" we will call complex anteriority; simple anteriority is the relation "Tr wholly before TO". We can then say that the basic use of the perfect is to express complex anteriority with non-deictic TO, while that of the preterite is to express simple anteriority with deictic TO.
The preterite vs the non-continuative perfect
As far as the three types of non-continuative reading of the perfect, deciding when to use them as opposed to the preterite is more involved. Here is the relevant section from CGEL (pp. 142-146):
5.3 Present perfect vs the simple preterite
■ Past time adjuncts normally excluded from present perfect
The present perfect involves reference to both past and present time: it is concerned with a time-span beginning in the past and extending up to now. It is not used in contexts where the 'now' component of this is explicitly or implicitly excluded:
 i I saw her last week/two minutes ago. [explicit exclusion of now]
ii Who wrote 'Moby Dick'? [implicit exclusion of now]
Except under conditions outlined below, time adjuncts like last week, two minutes ago, etc., which refer to times wholly before now, are incompatible with the present perfect: we cannot replace saw by have seen in [i]. Example [ii] illustrates the case of past situation focus: the existence of 'Moby Dick', and hence the writing of it, is taken for granted, and the issue concerns a particular feature of the past situation, the identity of the writer. Compare Who has written this note?, which might be said in a context where the note has just been discovered, with the focus on its present existence.[A special case of implicit exclusion is found in the use of the simple preterite for politeness/diffidence, as in I wondered if I could see you for a moment (§4.3.2). Have wondered could not be substituted here because it conveys (by virtue of the perfective aspectuality) that the wondering situation is over, which is the reverse of what I want to convey. (Progressive have been wondering is possible, however, because it has imperfective meaning.)]
5.3.2 The experiential perfect
Grammars commonly distinguish four major uses of the present perfect: the continuative, the experiential (or 'existential') perfect, the resultative perfect, and the perfect of recent past. These can be thought of as a classification of the main ways in which the concept of a time-span up to now can be involved in the use and interpretation of the present perfect—or as different ways in which the past situation may have 'current relevance'. The continuative has been dealt with already, and can be distinguished reasonably sharply from the non-continuative: compatibility with such expressions as ever since provides a criterion. The three categories within the non-continuative are not mutually exclusive, but they are useful nevertheless.
The experiential/existential perfect is seen in:
 i I've finally finished. We've now walked ten miles.
ii This is/That was the best meal I've had all week.
iii His sister has been up Mont Blanc twice.
This use of the present perfect is concerned with the occurrence of situations within the time-span up to now. The connection with now is clearest and most direct when the completion of an accomplishment takes place at (or virtually at) Td, as in [i]. [In spoken langauge, Td is just the time of utterance; in written lanuage, it is either the time of encoding (e.g. I'm writing this letter...) or the time of decoding (e.g. when you read the road sign You are now leaving Berlin); the 'd' stands for deictic.]
The possibility of having present time adjuncts like now or at present shows clearly that we have present time meaning as well as present tense form. These bear some resemblance to continuatives - the walking ten miles, for example, has occupied a period up to now. However, they cannot take continuative adjuncts like ever since (*We've now walked ten miles ever since we started), and they are interpreted perfectively, not imperfectively.
The connection with now is also apparent in [11ii], illustrative of a common type involving superlatives or ordinal numerals (cf. It's the first/third time you've said that today). There is an actual or potential series of occurrences within the time-span up to now (with first only one is actualised, but there could have been more). In the this is version of [ii] the meal is presumably still taking place, but it is nevertheless presented perfectively (progressive I've been having would be out of place), for the issue is its ranking in a series, which applies to it as a whole.
The connection with now is less direct in [11iii]: the ascents could be quite a long time in the past. The focus, however, is not on their occurrence at some particular time in the past but on the existence of the situation within the time-span. The connection with now is the potential for occurrence, or recurrence, of the situation at any time within the time-span up to now. Thus [iii] implicates that his sister is still alive, while I haven t been to the market yet implicates that the possibility of my going to the market still exists (it hasn't closed down).[The implicature may be weaker: that the same kind of situation is still possible. Nixon has been impeached, for example, can still be acceptable even though Nixon has since died, given a context where the issue is the occurrence within the time-span of situations of the kind 'impeachment of a president'.]
■ Experiential perfects vs simple preterites
Compare now the following pairs:
 i a. It is better than it has ever been. b. It's better than it was.
ii a. Have you seen Jim? b. Did you see Jim?
In [ia] the comparison is between its quality now and its quality at any time within the time-span—clearly the potential for it to be of such and such a quality still exists. In [ib] the comparison is between now and then; the past is contrasted with the present, the 'then' situation is over and excludes now.
Example [12iia] brings out the point that there may be limits to the time-span beyond those inherent in the situation itself. The inherent limit is that Jim (and you) must be alive, but in the salient interpretation I will have in mind a much shorter span than this: the time of his current visit to our vicinity, today, the period since we were last together, or whatever it might be. It would not be acceptable for you to answer yes on the strength of having seen him before this time-span. Whatever the limits on its beginning, however, the time-span stretches up to now. But [iib] is very different. Assuming again that you know Jim and have seen him perhaps many times, you need to determine more specifically what I am asking. This time, however, it is not a matter of placing limits on the start of the time-span up to now, but of finding which particular, definite past time I am asking about—your visit to Jim's sister last month, or whatever it might be, but a time that is over, exclusive of now.
■ Past time adjuncts in experiential perfects
This use of the present perfect allows for the inclusion, under restrictive conditions, of a past time adjunct:
 i a. He has got up at five o'clock. b. He got up at five o'clock.
ii a. We've already discussed it yesterday. b. We discussed it yesterday.
In [ia] "at five o'clock" is a crucial part of the potentially recurrent situation: the issue is that of his getting up at this early hour; there is no reference to any specific occasion, as there is in the simple preterite [ib]. In [iia] the already indicates that I'm concerned with the occurrence of the situation of our discussing it within a time-span up to now and cancels the normally excluding effect of yesterday evident in [iib].
5.3.3 The resultative perfect
 i She has broken her leg. He has closed the door. They've gone away.
ii She's been to the bank. She has run ten kilometres.
iii I've tried to phone her, but she's not answering.
The clearest cases of the resultative perfect are illustrated in [i], where the situation is one that inherently involves a specific change of state: breaking a leg yields a resultant state where the leg is broken, closing the door leads to the door's being closed, going away (from place x) results in a state where one is no longer at place x, and so on. The connection with the present in this resultative use is that the resultant state still obtains now. She has broken her leg does not mean "Her leg is broken", but this is the likely implicature unless the context selects an experiential interpretation. Cases like [i] are known more specifically as the perfect of continuing result: the resultant state begins at the time of occurrence of the past situation itself and continues through into the present.
Examples like [14ii] may be interpreted resultatively in a much vaguer sense. Be, as used here, means "go and return" and hence does not yield a resultant state "not at place x" as go does. A resultative interpretation of She's been to the bank is thus not derivable directly from the meaning but is heavily dependent on pragmatics—it might be, for example, "She has some money", but it could equally be "The cheques are deposited", or whatever. Similarly there is no state resulting inherently from running ten kilometres, so an implicature like "She is tired" or "She is hot" is heavily dependent on context.
Example [14iii] illustrates the phenomenon of 'nil results', the failure to obtain the expected or intended result—in this example, that of making contact with her. In the broader sense that goes beyond case [i], the resultative is clearly not mutually exclusive with the experiential: [ii] and [iii] have both components in their interpretation—and similarly
[13iia] is likely to have the resultative implicature "We don't need to discuss it again".
5.3.4 The perfect of recent past
 i It has been a bad start to the year, with two fatal road accidents overnight.
ii I've discovered how to mend the fuse.
iii She has recently/just been to Paris.
One respect in which a past situation may be connected with now is that it is close in time to now. It is clear from examples like [11iii] (His sister has been up Mont Blanc twice) that it does not have to be recent, but there is nevertheless a significant correlation between the present perfect and recency, whereas the simple preterite is quite indifferent as to the distance between Tr and TO ['time referred to' and 'time of orientation': Tr is here the time of climbing Mont Blanc, while TO is the time relative to which Tr is in the past; in this particular case, TO coincides with Td]. The present perfect is therefore the one most frequently used in news announcements, as in the radio bulletin example [15i]. It is arguable that the experiential and resultative categories are broad enough to cover all non-continuative uses, but recency adds an important component to the account. For example, [15ii] has a continuing result interpretation: the discovery resulted in my knowing how to mend the fuse and this knowledge persists. Such knowledge can persist for a long time, so there is nothing in the idea of continuing result itself to exclude my having made the discovery years ago. But in fact the normal interpretation involves a recent discovery. We have noted that experiential perfects like [12iia] (Have you seen Jim?) impose limitations on the time-span up to now beyond those inherent to the situation, and these additional limitations also involve recency.
■ Adjuncts of recency
As illustrated in [15iii], the present perfect admits the adjuncts recently and just, which of course signal a perfect of recent past (when they are used deictically, in contrast to the non-deictic use in She had recently/just been to Paris). But recency as such is not sufficient to sanction a time adjunct: *I have seen him a minute ago is no better than *I have seen him a year ago. Recently and just do not refer to definite times in the past, but indicate an indefinite time within a short interval stretching back from their TO ['time of orientation'] (which in their deictic use is identified as Td). They are comparable, therefore, to expressions like within the last few years, where recency is not an issue, but which combine quite freely with the present perfect.[There are some relatively small-scale differences between AmE and BrE with respect to the choice between the present perfect and the simple preterite—cases where AmE may prefer a simple preterite where BrE prefers or requires a present perfect. One case concerns situations in the recent past, where I just saw them, for example, might be preferred in AmE, I've just seen them in BrE. Another case concerns the aspectual adjuncts already and yet: for discussion, see Ch. 8, §8.]
And on pp. 712-713:
■ Still and already with the perfect
 i a. *He has still read the report. b. He has already read the report.
ii a. He has still not read the report. b. *He has already not read the report.
Already very often occurs with a positive perfect, as in [ib]: he is in the state resulting from earlier reading the report. We can't have still here: the state wherein he has read the report necessarily continues indefinitely, so it doesn't make sense to assert that it still obtains at the present moment. The negative [iia], however, makes perfect sense: the state wherein he hasn't read the report continues until he does read it.[Still also appears with the perfect in the 'progression' use discussed below: see [9a].] But [iib] is again excluded: as noted above, already in its primary sense does not take scope over a negative.
■ Use of still and already in cases of progression
 a. He has still read only twenty pages. b. He has already read twenty pages.
Still and already are often used of situations where it is a matter of progressing along some scale. Already suggests a relatively high degree of progression; still typically combines with only to suggest a relatively low degree. So far or up to now could be substituted for still and already giving He has read twenty pages so far; this says how many pages he has read during the period with now as terminal point, but without any indication as to whether this is relatively many or few. Already is often used with temporal expressions: It is already five o'clock, so he must be home by now. The low degree counterpart would usually have only by itself rather than still only, as in It's only five o'clock, so he won't be home yet.
■ Already for 'mounting process'
In the already example in , the suggestion of a relatively high degree of progression can be regarded as a special case of the implicature that the situation obtains at an earlier time than might have been expected: there has been greater progression than might have been expected. In other cases, however, it is not a matter of the situation obtaining at an earlier time than expected, but of it being a stage in a potentially mounting process:
 i He already owns two newspapers and a TV station: this takeover must be stopped.
ii There is now at least an even chance that this nation of almost 200 million
people will shortly erupt in murderous violence. Already, protests of various sorts
have taken place, mostly in provincial cities.
iii It isn't clear whether Brazil, which already wasnt making payments on the
principal of its foreign debt, will come out of the moratorium in a better state
to service its debt.
An undesirable situation obtains at the time in question, and it is envisaged that things may get worse. In this use already can be placed in front position, as in [ii], or have scope over a negative, as in [iii].
■ Already and yet with a perfective
In BrE, and some varieties of AmE, the aspectual adjuncts are restricted to imperfective situations, as illustrated above. Other varieties of AmE, however, allow already and yet to occur in perfective examples, as in:
 i A: Can I speak to Ed, please? B: %He already left yesterday.
ii %Did he leave yet?
Already may also follow the verb: %He left already (with main stress on left). This use of yet (criticised in some usage manuals) is restricted to informal style.
R. Huddleston and G. K. Pullum, The Cambridge Grammar of the English Language (Cambridge University Press, Cambridge, UK, 2002).