I'm just wondering what an appropriate period is for looking for an answer to a particular problem (both here and elsewhere) before asking on an SO site? Usually the questions I've asked have been answered in 10 minutes or so, so it really makes no sense to spend an hour trying to solve a problem before asking. What is a general consensus?
It really is up to you.
I personally prefer to spend half an hour to an hour at least trying to figure it on my own, since as a side effect I usually learn quite a lot more than just the solution to my problem.
However, if you are in a tight schedule and have a deadline looming over you, do a quick search on SO and ask right away if you don't find anything.
As long as it takes you to do a good Google search, or two, to try and find the solution on your own. But in reality, it doesn't much matter as there is no conceivable way to verify that you waited at all.
BTW: Welcome to SO, don't forget to read this post: https://stackoverflow.com/questions/18557/how-does-stackoverflow-work-the-unofficial-faq
At the least do a Google search. I've noticed numerous questions here where the accepted answer was copied verbatim from the first hit on a Google search for the question title.
It's also useful to put in your question the steps you took and, if applicable, possible solutions that have already been rejected.
Search here first, and if you find a similar question that doesn't suit, ask your question here, reference the other question and say why it doesn't suit. Personally, I'd ask here and google. I'd also tend to have a rummage around the CodeProject, Source forge, and Code Guru. Some very good programmers will spend more time on one site than another, so it's worth searching them all. I've had some great answers here but also drawn some blanks. Using SO exclusively, will IMHO make you less resourceful in the long run. Just because it is a great site, that is not an excuse to be lazy.