This is surprisingly confusing! Probably the biggest difference is that NOT makes a verb negative. "I do NOT want to eat now."
If your noun has an article (A, AN, THE) you use NOT with it, as in "I am NOT the person you think I am." Without an article you use NO, as in "There is NO money left to spend."
I'm sure there are many other examples of when you would use one rather than the other, but these are the ones I can thing of now.