1. Google
2. Stare at ceiling.
3. Do something unrelated, like read HN, while my subconscious ruminates.
4. Try again.
In addition to that, I sometimes try IRC (Freenode) as well.
The intention is to have a core group of hackers essentially leave it on all the time and answer when available. When it works, it is much faster and often more useful than forums/Google.
If interested in beta-testing before full release, please email. We obviously need a core group of interested parties.
Some more info on it:
http://www.ics.uci.edu/~jpd/classes/ics105s03/readings/acker...
at MIT had almost exactly the opposite problem: people were charged up/competing to be the first one to provide the correct answer. It worked shockingly well, as a consumer and it was fun to kill some time as a supplier of answers. (My time at MIT all pre-dates the interwebs, so I can't directly compare/contrast it to a world with Google as an option.)
For some problems, though, it's harder to search for an answer. For example, a question of good javascript style for a particular thing you are trying to do. For this sort of thing I ask friends of mine.
There's also generally mailing lists and forums that are appropriate for your specific topic. Stack Overflow too if your question doesn't fit nicely into a topic. The problem with these is that you generally don't get an immediate answer, and you might not get an answer at all, so you have to kind of ask your question, then keep trying on your own anyways, or do something else for a while. So this is definitely not as good as the instant methods. You also are more likely to get bad advice if it's not from someone you trust.
I never use books to solve specific programming problems. Much too slow. Maybe if they were searchable.
These are just a few of the populated and extremely helpful channels available.
As Tichy alluded to, I make heavy use of IRC in what I have learned to be are some polite and efficient channels. It takes a while to see which channels are going to help you and which are just going to waste your time, although the latter is easier to spot.
Sometimes I find forums to be too slow and good only for search purposes - in IRC, if I have a problem with Linux, Windows, or a programming language that can't be easily found in a timely search session, then there are an abundance of folks willing to help out in real-time. A lot of folks knock IRC for the shit that tends to float around, but I just keep my client open all the time and then go to it when I need to ask a question. It's kind of like my own support team that I haven't paid for in terms of currency. If you've served your time over the years, such as helping others out, then your service will be answered in kind when you have a problem - it's almost like a respect has been built upon, folks remember you; some channels have karma points to increase the reputation of active helpers.
Some of the best professional working relationships I've built have come from IRC, which these days I talk to and consult via direct IM, say with Pidgin instead of clogging the channels.
If you decide to use IRC, I have the same handle there too. :) Hope to see you there!
Mailing lists that are specific to the larger issue, such as a list for a framework, in my experience have shown to be more helpful than forums... your results may vary.
For Rails I have found that just browsing the source/comments on github is the best source for figuring out really tricky issues. I stay logged in to IRC but most of the time never feel like bothering anyone. I kind of enjoy figuring things out for myself, even if it's a trivial problem I still get satisfaction from solving things on my own.
Edit: Also, friends smarter in whatever area it may be, if any are handy.
1. Google
2. Whiteboard
3. Flatmates