First off, is it reproducible? That's a HUGE plus if it is. I want things bugs to always/never happen... its the intermittent ones that are the troublesome ones.
And it is going to depend on the problem, but at my shop we'll generally tag-team such a problem figuring that 2 heads (or 3 or 4) is better than 1.
Occasionally the bug won't even be in MY code, but it generally is. There have been issues where a 3rd party library was the culprit or a particular implementation on a particular platform was the cause - those stink.
I'll use anything and everything to at least track it down: debuggers, trace output, whatever.
Typically, if I can isolate it to a class or module I'll write a test harness to duplicate the real world and try to duplicate it there. I generally write my test code first, but sometimes legacy code (or other developer's code) exists that doesn't have tests already.
I generally will talk the design and problem through, out loud with the team and whiteboard anything that isn't clear. Often the solution will bubble to the surface once we talk about it as a group.
That's what I do.