My toilet is running. I checked the round rubber piece on the bottom (the Pluggy Sealer) and it's tight, no water escaping. The water is filling all the way up and then flowing into that pipe (Mr Thirsty). The thing that floats up with the water and supposed to stop the water from flowing (Floaty McTopper) is going all the way to the top but not stopping the water from flowing.
What needs to be replaced?
(sorry if I used a lot of technical terms)
If the flapper which is used on the bottom covering the hole where the water escapes is fine then your next option is to check on the float with the ball(Balloon shaped) or if newer toilet then there's a little round or circle float device that controls the rod, if you pull up on the rod and it stops you know the float thingy is broken, either you can buy a generic replacement from a plumbing supply store or from home depot, or if it's a Kohler toilet or some other brand you mind find a diagram on the back of the cermaic cover going on the back of the toilet with all the parts and part numbers, and then you can google that part.
Also if you know what your doing there's a way to reposition the float to stop the toilet from running earlier and put less water in the tank, you should be able to adjust a screw somewhere on top of the float mechanism.
Play around with the float and see what works.