Could be a number of things:
Water level set too high? If it is, water will flow into the bowl the whole time, and the float can never shut off
Flapper not sealing? Same thing - continuous flow to the bowl. This can be caused by a bad flapper seal, or the pull chain too tight - needs to have some slack in it.
Really hard water? Deposits could be keeping the shutoff from closing tightly.
Cheap fill valve assembly? I made this mistake once, one of those types that has the float "hidden" inside a housing instead of at the end of an arm - stupid thing would never get a good shutoff against water pressure. Replaced with a better float design and problem went away.
Take the lid off, and use your finger to push down on top of the fill valve - does the water stop? That's usually a good sign that the fill valve isn't getting a good seal