"Do" vs. "does" with multiple singular subjects

The correct way to ask that question would be with "do". Consider these two examples:

How does StackOverflow connect to ServerFault?

In that case one item is being considered. Now what if we change the way the verb connect is being used a little and add a second part to the subject so that it is effectively plural:

How do StackOverflow and ServerFault connect with each other?

Although in both cases the verb "connect" is being used, in the first case the subject being discussed is singular and in the second the two part subject is, considered as a whole, plural.

The giveaway would be if you dropped the specific names and just asked your question with the word "sites":

How do sites connect together?

When switching from a singular to a plural subject, the helping verb does need to change.

I have to disagree with Ham and Bacon's answer; the correct verb is "do". The reason I believe his answer is not applicable is, he's talking about a list of countable direct objects; your construction is talking about an uncounted collection of subjects. (I'm not sure which of those distinctions makes the difference at the moment. :-) ) Nobody, I hope, would think of saying "How is John, Jim and Joe doing?". Similarly, if you simplify your own sentence a bit, you get "How does Serverfault and StackOverflow connect?", which should sound wrong to any trained native ear. Serverfault and StackOverflow (and the others) are a group, and even though they are individually called out, they are still being treated as a collection grammatically, and therefore take the plural verb.

This should be

How do serverfault, stackoverflow and other stackExchange sites connect together?

because "sites" is plural so the verb should also be plural. The names of the sites shouldn't confuse things; you can treat them as adjectives. If you drop them out, you have

How do [these] sites connect together?

If you put does in this place, it is wrong because it does not match the subject.