For me, IRC, message boards, etc. I also think reading documentation is something that one needs to learn, and often answers a lot of questions. Even before Stack Overflow existed, I saw many ignore the documentation that was often right in front of them.
You collected books on the programming language or system APIs, or a textbook on algorithms, and sometimes saved magazines, plus a bit of experimentation.<p>Fidonet and Usenet were good places to ask.<p>Looking at the source code of open source projects, especially when some piece of the code was doing something that you wanted to figure out.
Various magazines (Dr. Dobbs, MSJ/MSDN Magazine), USENET (comp.lang.*), email lists, MSDN subscriptions (the DVDs full of Microsoft documentation), books, lots of experimentation, etc.<p>There were actually quite a few resources before StackOverflow.
You solved problems yourself.<p>Truly, a dark time compared to the more enlightened "cut and paste from some website solves all problems" utopia we now live in.
For a lot of internal code in large companies, stack overflow does not help.<p>Tribal knowledge and becoming a ninja at debugging and reverse engineering ancient code seems to do the trick.