Killing moles in your garden or lawn is about as hard as winning the lottery it seems, but people have done it. I have heard success stories from individuals who went online a bought the latest DIY mole control product like Talpirid or some other kind of trap or device and won the battle. Those are the lucky folks, then there is my Barber who has a house down the shore and is in a constant battle with these creatures. Controlling moles in a lawn is not easy, but it can be done. Personally I would recommend calling any number of experts in the field. Locally there is a company called the Mole Man who sole purpose it to get rid of your mole problem. I am sure there are other companies in the USA who also specializes in mole control.
If you are adventurous or want to go crazy like the guy from Caddy Shack then order your products and say a prayer. If you catch the problem early enough then maybe you have a fighting chance. Sometimes it is as easy as eliminating there food source by treating your lawn for grubs and worms early in the season and starve them to death (or at least drive them over to your neighbors). Anyway...happy hunting and god luck.