I let my dogs hunt them. This is especially convenient because not only do the dogs kill the ground squirrels, they dispose of them (i. e. eat them) too! If you choose to take this route be sure to worm your dog regularly.
There are three main methods, Habitat change (removing anything that they can find cover), Lethal (poison that is legal without a professional), and a trap.
You can eliminate ground squirrels most efficently by trapping them. Depending on your preference you can humanely trap and release elsewhere or you can trap to kill. You have to remove enough so they cannot breed.
The best thing you can do is to not feed them. Don't put things out for them to eat. They will get into bird feeders too. You should get live traps and then let them go in other wooded areas far enough from your home that they won't come back.
