Turn off the water supply to the toilet. There is a flexible pipe that runs from the floor or wall to your toilet tank. This pipe has a faucet or lever on it that allows you to cut off water to the toilet.
Remove the cover from the back of your toilet and place it on the floor. Look inside the tank and you will see an assembly that includes a round valve at the bottom center of the tank.
Flush the toilet. Because you have turned off the water supply, this will empty the storage tank and it won't refill.
Remove the valve from the bottom of the tank. Different valves are connected in different ways, so inspect your valve carefully to figure out how to remove it without breaking anything. A flashlight is helpful in this process.
Inspect the opening at the bottom of the tank, looking for mineral buildup. Inspect the valve itself, especially the bottom, looking for mineral buildup, rotted rubber or anything else that might indicate a reason that it isn't seating properly and is allowing water through.
Remove all mineral buildup, clean the valve and reattach it. Turn the water back on and pay close attention to the toilet for a few hours to determine if it is still running. If the problem persists, remove the valve and replace it with a new one, which you can purchase inexpensively at any plumbing supply or home improvement store.