Tank does not fill after flushing?

In the tank, you probably have a fill valve that has a round float that goes up and down on a shaft. There is a washer in the top of these that gets hard or plugs and will not let water in. The most common one of this type comes apart at the top and the washer is in the bottom part. A little bigger than a quarter with a small rod in the center. Replace this and the toilet should fill. It comes apart by holding the shaft so that it doesn't break and twisting the top 1/4 turn counter clock wise. Shut the water off before you do this.