A good place to start is with simple and useful regexes. Decide what you want to do then set about learning how. Firstly look in google for the spec of regex and how it works, then look for solutions to your specific problem. Pull apart each part of the solution and reference it against the spec of regex to see what its doing. Then i'd try make one myself, if i couldnt get it to work id repeat the first step for assistance
I just think of something I want done, go on Google to find if anyone has explained something similar, then adapt it to my purpose, then figure out WHY it works (if it does). It can do a remarkable amount of stuff; try to think of harder and harder stuff to do, and try to see if you can make it work. Good luck!