One of the best things you can do is thicken up your turf. I do lawn and tree care for a living, and I see a huge difference in yards where moles are, depending on what the homeowner does. On a yard with a healthy root system, the damage is much less severe. Often the grass will not die and may discolor at most. Good watering, fertilizing, aeration, and proper cutting are key. Your plan of action may be different depending on where you live and what grass types are there, but the general idea is the same. Healthy roots mean fewer weeds as well.
It is ironic that good lawn care does bring some critters.
