Suppose I'm talking about some design scheme. I say something like "foo was once designed and implemented in a way called bar that ...". Then I want to introduce the original scheme "bar", for example, "in the bar method, foo ...". To describe the behaviors of "foo" in the old design scheme, what tense should I use here? And are there any general rules about these cases?
In technical writing (and indeed in most expository writing) the best rule I've found to be useful is tense consistency.
So if you say
foo was once designed and implemented in a way called bar that required X to do Y
you should continue along the lines of
In this scheme, bar caused farf to jiff and klurg was responsible for regulating the status of kling..."
i.e., continue with the past tense.
Then, when you move to describing the new way of doing things, you can choose present or even future. They have different connotations. Here is the future option:
In the new system, foo will be implemented by first jiffing and then kluring the inputs, after considering the status of bar. Bar will take the place of shlimpf when vlerg finishes.
Choosing the future case requires that the implementation work has not yet been done, and maybe that the whole setup is open to revision. But you can also use the present tense in this case, especially if you are trying to resist revisions. And you would also use the present in the case where the implementation has already been done:
In the new system, foo is designed and implemented by first jiffing and then klurging the inputs, after considering the status of bar. Bar takes the place of shlimpf when vlerg finishes.
(Notice that the present tense of passive verb forms end in -"ed"; it's the auxiliary (is vs. was) that determines the tense of passive forms.)
Could you use the past tense as well? Consider
In the new system, foo was designed and implemented by first jiffing and then klurging the inputs, after considering the status of bar. Bar took the place of shlimpf when vlerg finished.
There are two problems here. The bigger one is that the choice of tense in the second sentence is incorrect. The second sentence describes a continuing tendency, rather than a result (something done and over with), and so by the general rules of English grammar the past tense is prohibited. But then the first sentence sounds too disjoint with respect to the second if you leave it in the past tense, so converting it too to the present tense improves the whole thing.
The second problem with retaining the past tense is that even if you dropped the Bar sentence, the effectiveness of any contrast you are making between the past way of doing things and the present way of doing things is undermined by sharing the same tense between the two discussions. It is easier to confuse the two, especially when jumping between different parts of a document.
Finally, if you don't discuss the earlier system at all, the present tense is generally preferred anyway, on the basis that it makes descriptions more vivid and engaging than the past tense. Though it can feel manipulative when used to construct narratives of one-time events, it never has this feeling in the kind of technical writing you are describing.