I highly recommend working with other programmers if you are hitting a roadblock. Often the conversation goes something like this:
[you] I'm stuck on this bug, I can't seem to figure out what's happening
[other] What's the issue?
[you] yada yada yada
[other] what have you tried and what have you figured out so far?
[you] blah blah blah, this that and the other...
[you] oh...
[you] thanks!
[other] any time
If not that, often a more senior person can help you narrow down your approach or sometimes mention some little-known or unintuitive facts about the relevant context.
Another crucial piece is to divide and conquer. You need eliminate possibilities or you will end up going in circles. That goes hand-in-hand with testing your assumptions. When you get into a situation where you can't figure out why something is happening, it's likely that something you believe is true is not true. Start testing all the things that you think are obviously true.
Be wary of debuggers. They can be helpful for novice developers but can end up consuming a lot of your time. Also, they are mostly useless for timing issues such as multi-threading problems. I once had a (very smart) colleague who completely disagreed with me and insisted on using debuggers. Once he had an issue that he couldn't figure out. I asked him to run it without the debugger. He did and the problem disappeared.
