Inside your toilet you have three places where your toilet could leak the fill valve the overflow and the flapper.

If the fill valve is the issue the water will keep filling untill the water goes into the overflow tube and leaks into the bowl.  Connected to the fill valve is the ball.  The ball should lift and turn the water off typically an inch below the overflow.  An easy way to check if this is the problem is to shut the water off.  If the water stops running chances are its the fill valve.

If the toilet fills, stops and then fills a few minutes later then the issue is either the flapper or the overflow.  Most likely its the flapper, remove the flapper from the hooks and hold it up.  If the rubber is bent then it is more then likely causing the issue.  If the flapper and fill valve are both ok then the next step would be replacing the overflow. This repair can be a little more extensive and at this point you might want to consider replacing the whole toilet.