Most likely you just need to change the seal on the flush tower. (The least expensive solution, and it's usually all you need.) It's easy to do with the Korky 427BP replacement seal. See my responses 9 and 21 in this thread: http://www.terrylove.com/forums/show...Stops-Running/ The suggestion made by Redwood that I link to in response number 21 is a little trick for getting the seal on correctly. The guy I was helping tried the trick after not getting the thing to stop running after replacing the seal, and the trick worked perfectly, so all the discussion about new flush valves, etc., was totally unnecessary. All he did was replace the seal, and then use the trick to make it seat properly, and for a couple of bucks he was leak-free.
If you need me to break it down more for you, just ask.
Good luck and let us know how it goes.
(Unlike the guy in that thread, you most likely do NOT need a new fill valve as well.)