Here is a quick review of the advice that four influential style guides give for punctuating the lead-in to a display (vertical) list. The most important thing to note at the outset is that most of the style guides I consulted do not view the presence or absence of the particular words "as follows" as being critical to the guidance they offer. Rather, they see the key question as being whether the lead-in constitutes a standalone entity (usually, a complete sentence) or whether it constitutes a fragment that develops into a complete sentence over the course of the list that follows.
From The Chicago Manual of Style, sixteenth edition (2010):
6.124 Vertical lists—punctuation and format. A vertical list is best introduced by a complete grammatical sentence, followed by a colon (but see 6.125). ...
[Partial example 1:]
Your application must include the following documents:
a full résumé
three letters of recommendation
all your diplomas, from high school to graduate school
[Partial example 2:]
Compose three sentences:
To illustrate the use of commas in dates
To distinguish the use of semicolons from the use of periods
To illustrate the use of parentheses within dashes
[Partial example 3:]
To change the date display from "31" to "1" on the day following the last day of a thirty-day month, the following steps are recommended:
Pull the stem out to the time-setting position (i.e., past the date-setting position).
Make a mental note of the exact minute (but see step 4).
Turn the stem repeatedly in a clockwise direction through 24 hours.
The exception that CMoS presents in section 6.125 is as follows:
6.125 Vertical lists punctuated as a sentence. In a numbered vertical list that completes a sentence begun in an introductory element and that consists of phrases or sentences with internal punctuation, semicolons may be used between the items, and a period should follow the final item. ...
[Example:]
Reporting for the Development Committee, Johnson reported that
a fundraising campaign director was being sought;
the salary for this director, about $50,000 a year, would be paid out of campaign funds; and
the fundraising campaign would be launched in the spring of 2005.
Interestingly, CMoS doesn't bother to point out that the introductory fragment leading into its numbered list in 6.125 takes no punctuation at all. In effect, the vertical list is simply a broken-out version of a longish sentence, in which the writer treats each parallel clause as a separate entry in the list and adds a sequential number to the beginning of each entry.
As for the examples in 6.124, it seems clear that a writer could—with a bit of editorial rejiggering—rework introductory sentence in each case to end with the words "as follows," without having any effect on the style guide's advice to follow the complete sentence with a colon. For example, in the first instance you might reframe the sentence as follows:
Your application must include several documents, as follows:
With regard to "as follows" in run-in text, CMoS offers this guidance:
6.62 Colons with "as follows" and other introductory phrases. A colon is normally ued after as follows, the following, and similar expressions. [Cross-reference omitted.]
[Example 1:]
The steps are as follows: first. make grooves for the seeds; second, sprinkle the seeds; third, push the earth back over the grooves; fourth, water generously.
[Example 2:]
Kenzie's results yield the following hypotheses: First, ... Second, ... Third, ...
The Oxford Guide to Style (2002) doesn't address the question of how to punctuate the introductory sentence of a vertical list, but in its section 9.1.4 ("Displayed lists"), it presents three examples of displayed lists and in each case introduces an example list with a complete sentence followed by a colon. Here is the first example, with its lead-in:
In the so-called hanging list, turn-lines and any subsequent lines hang from (align on) the start of each line of text:
The cerebellum forms two spheres—one on each side of the central region (vermis)—and is overhung by the occipital lobes of the cerebrum.
The pons (Pons Varolli), linking the medulla oblongata and the thalamus, bulges forwards in front of the cerebellum.
The medulla oblongata (myelencephalon), the extension within the skull of the upper end od of the spinal cord. forms the lowest part of the brainstem.
And here is Oxford's example of an unnumbered (bulleted) list, again with text lead-in:
Here are two examples of unordered lists:
Bulka
Hundertspiel
Špády
Trappola
Evidently, Oxford is following the same formatting approach that CMoS recommends.
Bryan Garner, Garner's Modern American Usage, third edition (2009) addresses the question of how to punctuate the lead-in sentence to a list somewhat glancingly, in the course of a discussion of how to use bullets as punctuation marks:
Here are seven more tips on using bullets well: (1) end your introduction with a colon, which serves as an anchor; ...
Garner returns to this use in his section on colons:
Second, the colon can introduce a list of items, often after expressions such as the following and as follows—e.g., "The meetings are as follows: Central, Dec. 11 at the Municipal Auditorium, 5:30 p.m.–7:30 p.m.; South, Dec. 15, at the Mexican Cultural Institute, 5:30 p.m.–7:30 p.m." [Citation omitted.]
For purposes of the poster's specific question about "as follows," Garner offers one of the most relevant discussions that I found. Garner also emphasizes that a colon can follow an introduction to a list even when that introduction is not a complete sentence. Here, for example, is an extreme instance from Garner's discussion of the uses of a colon:
First it [the colon] may link two separate clauses or phrases by indicating a step forward from the first to the second: the step may be from an introduction to a main theme, from a cause to an effect, from a general statement to a specific instance, or from a premise to a conclusion. E.g.:
"Boeing left some chips on the table: It agreed to give up the exclusive -supplier agreements it had negotiated with American Airlines, Delta Airlines, and Continental Airlines." [Citation omitted.]
"Economists point to day care's problem as a classic case of market failure: ... [Citation omitted.]
"My assignment: Identify and contact the CIOs for 100 companies that were selected on the basis of their productive and innovative use of information technology." [Citation omitted.]
Clearly, Garner sees no reason to adhere to to CMoS's stricture that "A vertical list is best introduced by a complete grammatical sentence, followed by a colon"; if you can introduce a vertical list with "E.g.:" you can introduce it with anything—and yet Garner is careful throughout his style guide to complete the introductory sentence, phrase, or other term before a display list with a colon.
Finally, Words into Type, third edition (1974) offers a somewhat different take on proper end punctuation of sentences or phrases that introduce display lists:
Lists. A colon is used after an introductory statement that contains the words as follows or the following; either a colon or a period may be used after other statements introducing lists.
[Example:]
We will discuss the following types of psychotherapy:
Client centered therapy
Rational-emotive therapy
Behavioral therapy
When the introduction is not a complete sentence and one or more of the items of the list are needed to complete it, no colon or dash should be used.
[Example:]
Two types of psychotherapy are
Client centered therapy
Rational-emotive therapy
An exception to the foregoing is that a colon may be used to replace a comma when the statement preceding a displayed list ends with such words as for example or that is.
[Example:]
We have thus for covered two types of therapy, that is:
Client centered therapy
Rational-emotive therapy
I don't know why Words into Type thinks that the words "as follows" or "the following" require a colon, whereas the same sentence without those words can be punctuated with either a colon or a period, but that's the position it takes—and this book was very influential in the publishing world in the late 1900s.
In other respects, Word into Type seems much more welcoming to the use of a period rather than a colon at the end of an introduction to a list than (for example) CMoS and Oxford are.
Conclusions
How you punctuate the end of an introductory sentence or phrase preceding a display (vertical) list is ultimately a style question, as all punctuation questions are. The goal of punctuation is to guide readers as subtly as possible to a clear reading of what the author is trying to say. But for that very reason, aiming for the mainstream of punctuation conventions is a good idea: you don't want to leave your readers in a pathless jungle of unpunctuated prose, but you also don't want to distract or baffle them with baroque or idiosyncratic punctuation choices.
In the case of introductions to display lists, the least-disapproved end punctuation mark in the four style guides I consulted is the colon. Indeed, Words into Type insists that it is the only appropriate punctuation mark to use at the end of an introductory phrase that includes the words "as follows." Other style guides are less particular on this point, but not one objects to using a colon at the end of introductory sentence or phrase unless the following list is really just a complete sentence chopped into parallel pieces (in which case, the style guides that address that exception recommend using no end punctuation before the list at all).
Although my answer has focused primarily on display lists, the argument for using a colon before the first entry in a run-in list is essentially the same, and (as CMoS 6.62 suggests) the appearance of "as follows" in the middle of a paragraph usually signals a fairly complex string of parallel entries (whether sequential instructions or a list of examples) that would benefit from being demarcated by a preceding colon.
