I have never had a mole problem till I moved to the country, my yard was full of them
Moles will destroy your yard, they leave big holes that are not only unattractive but can also be dangerous if you step in them, they also leave unsightly trails in your yard, that usually lead to the "den" where most of the time you can catch these little critters and hopefully take care of the problem.
There are different mole traps that you can use to trap them in and relocate if you choose not to kill, to me harpoon trap is going to be the easiest to use, also I have found using traps and trying to relocate does not solve the problem they usually come back.
Hardware stores carry a poison called Vengence bombs this works wonders ... it is going to kill the moles but it will also take care of your problem.
In the end ridding your lawn of these critters is to find a solution that works for you. Bytrying out different types of treatments you will find one that will restore and give you back your yard.