The first step to take is identifying what animal or rodent is causing the damage, this way its easier to find the best deterrent for it. For example, is the animal drawn to a certain food source found in your yard? Perhaps there are certain types of plants or shrubs it enjoys. If you find this to be the case, it might be better to remove them from your yard. You might also try a barrier method around the perimeter which is designed to keep out wildlife. Try using some type of visual deterrent or even a noise that will frighten the creature away.
As a last resort, capturing and relocating the animal is an option. If you do decide to do this, however, it would be best to first consult your local animal control or wildlife agent who will be able to advise you on what to do. Finally, after considering all your options, you might decide that the animal is not that much of a nuisance after all and the best course of action is to take no action at all.