For moles, if you get rid of the grubs they're eating, they'll generally go away. Gophers eat roots, so getting rid of the grass isn't really an option; I've had good luck with the poison gas sticks. The name escapes me, but they're about 6" long, 3/4" diameter, and you light them before sticking them down the hole.
If it's a gopher set a gopher box trap in an open hole and you will normally have him in a couple of hours...If it's a mole then the mole trap will cost you several dollars ( mine was around 15 or 20 dollars) and it takes a little longer to get him, but it's all worth it when you look out in your yard and see the trap has pinned him to the ground..the mole trap has no mercy on the little guy.....