Your problem is that the float (ball on rod) is not adjusted low enough so that when it floats up it doesn't exert enough pressure on the cutoff valve to completely stop the flow OR the valve is so corrupted with mineral deposits that the float arm cannot exert enough pressure. There are DYI methods to correct both conditions; however, the best, easiest, fastest way is to go to your locally-owned hardware store (they're all members of buying groups and their prices on such common items are almost always lower than the discount stores) and purchase a complete kit (float, flapper, and valve). Easy-to-follow instructions are always on the package; installation takes no more than 1 hour for the most inept DYIer. If you can read and know about "righty-tighty, lefty-loosey," it should not take more than 15 minutes. It is helpful to have a wet pickup vacuum handy; use it to remove water that remains in system after turning off water supply and flushing. Or you could call a plumber for $150-250.
