I have holes in my yard about the size of a quarter with a little mound of dirt around it. What is causing this and how can I stop it?

Many kinds of animals create holes in the ground without leaving any sign of the soil that was excavated. If the holes or burrows are not active, the best you can do is guess about the identify of the digger.
Thirteen-lined ground squirrels and chipmunks dig burrows (typically) without leaving soil at the entrance. However, the entrances to their burrows are usually more than an inch in diameter. The burrow entrances of voles or shrews are smaller often around a dime to nickel size.

Because the holes are so large, it is difficult to determine what may have caused the holes accompanied with circumferential mounding. Crayfish and worms can create such mounds but their holes are not quarter inch in size. Chipmunks and thirteen-lined ground squirrels make holes that sized but no mounds. It is possible that they were made by some kind of insect. I have no idea what that insect might be.

You may want to contact your local Extension Office directly.