Actually the question might be most interesting when one is neither a PhD nor an established professor. I would like to know the answer myself, but one thing I try to do is to read a lot of conference abstract in areas close to what you are doing. For my field, which is commutative algebra, there is a nice website which has a pretty comprehensive list of conferences, and I imagine other areas would have similar sites.
Other than that, one could try to do the normal things more thoroughly. Say, if I am working on some problem about "local hypersurfaces with isolated singularity", I would also search Math Sci Net for "smooth projective hypersurfaces" as well. I have learned quite a few useful things that way. And don't be shy about approaching people you don't know personally with questions about your or their work, even via emails. I found the majority of people are happy to tell you what they know.
Finally, one way to find out if other people are working on the same thing as you do is to advertise what you are doing. So putting your pre-prints/slide on arxiv and your website and give as many talks as you can would presumably help.