I, too, have a kidney stone.
It's actually in the kidney, and it only causes me grief every so often (this past week, definitely).
Definitely stay hydrated (which may have been my problem, recently - I may have slacked off on the fluids).
Mine isn't going to go away any time soon, but the doctor says that ones in the kidney don't often cause as much problem, but operating would possibly cause more problems than they want to deal with, so it stays where it is. It's way too big to pass through the tubes.
I don't follow any specific diet, although at first I had read up on it and wondered about the wisdom. However, I'm not trying to tell you what to do, because everybody's situation is different.
The advice about seeing a nutritionist is a good one, and worth following.