There are many makes and models of toilet, but the flapper-valve assembly will look basically the same. Removing the rubber flapper from the assembly is easy. Some snap off and require no tools; others are held in place with a machine screw.
Although generic flappers are available, stick with the part made for your toilet—provided you can find a replacement. Note the brand of toilet, and take a look at the valve assembly before you shop. Better yet, take the flapper with you to be sure you get the right one. Plumbing jobs are famous for prompting repeated trips to the store for more parts. But there's no need to visit more often than you really have to.
Shown: The flapper on this flush assembly pops off without any tools. Simply replace the old flapper with a new one. Be careful not to break off the barbed plastic pin.