Moles are notoriously difficult to exterminate because they are not attracted to rodent bait and they often burrow deep into the ground, making them difficult to reach. Moles subsist on earthworms, which are ubiquitous in soil. While they do feast on the occasional grub, ridding your lawn of grubs will do little to fix your mole problem. And "quick fixes" do not work to rid your lawn of moles. The only way to remove moles effectively is to use bait that attracts them or to remove them physically.
An effective bait is one that is in the form of a worm. The smell entices the mole, and its poison, Bromethalin, kills it. There are two types of traps that are effective for trapping moles. Scissor traps work best when the mole is deep below the ground. Harpoon traps are easier when the mole's tunnels are close to the surface. Mole bait and traps like these are available at most hardware, farm supply, and home repair stores. They are generally amidst a variety of mole control products that are ineffective. Ensure that what you are buying is, indeed, something that will be effective.
Where you place your bait or traps is critical. Choose a "run"—or tunnel—that the mole uses regularly. These runs are usually straight as opposed to curved or "squiggly," as they are typically used only for food foraging. The best straight runs follow structural guidelines, like gutters or curbs: the mole uses this type of run to move from its nest to its foraging ground. To determine if the run you have is one that is used regularly, stamp it down and return the next day to see if it is pushed back up again.