Go to Lowes or Home Depot and pick up a Fluidmaster toilet tank repair kit and a flex toilet supply line to connect to the water line afterward , It comes with ALL the parts to completely rebuild the toilet tank and it is very easy , After shutting the water off , Flush the toilet to empty the tank , Then suck out the remaining water with a shop vac , Just follow the step by step instructions , Be careful not to overtighten the tank bolts when installing the tank or the tank will crack , Good luck, I'm sure you can do this without a hitch
First put a few drops of food coloring in the tank. If it shows up in the bowl replace the flapper. Then put a few drops of a different color is the overflow. That is the quickest way I know to see what element is leaking! When it doubt rip it out and replace the guts!