I tried to write out a few tips, but didn't know a lot of the terminology and such. This link is probably simpler, as it has photos and a video and such (and they actually know the terminology):
Not exactly sure what you mean by still runs without flush but there are two things that can cause a toilet to run on, or mimic the sound of a flush every once and a while.
One thing is the flapper in the tank. As they age they sometimes become warped not allowing the rubber flush device to seal tight against the opeing that allows the water to flow into the tank when you flush. As the water begins to drop this all of a sudden causes the flush falve to turn on and make the same sound as though you just flushed the toilet.
The other thing is the water in the tank is to high and the execssive water in the tank allows water to flow into the overflow pipe in the tank making a running water sound. This is fixed by adjusting the height on the float within the tank so it turns off the water before it begins to overflow into the overflow pipe.
Bob has you covered Bonny. What kind of toilet and how old are the internals on i? We find that flappers deteriorate every few years and need to be replaced. If the leak is at the overflow tube and you have the "ball" type float, you can usually adjust those to the proper level.
Bonny what Woodbridge says, plus if the refill tube is stuck down in the overflow below the water level it will siphon water out of the tank causing the water level to drop and turn on like you just flushed the toilet.