The best way to prevent armadillos from getting into a yard and destroying the lawn is erecting a fence that doesn't have spaces that are large enough for the armadillos to crawl through. It should be deeply buried in the ground to ensure that the armadillos cannot dig under it.
While fencing is the most effective way to keep armadillos out of the yard, it is also the most expensive way. Armadillos are known for their acute sense of smell, so a good way to ensure that they do not destroy lawns is to sprinkle vinegar or ammonia around the yard. Pine needles and pine bark also give off a scent that is repulsive to armadillos. Add these needles or pieces of bark to garden fertilizer and sprinkle it throughout the garden and the lawn to ward off armadillos.
A number of devices are available for purchase that are specifically designed for trapping armadillos. These traps catch the armadillos without killing them so that they can be relocated to a more fitting habitat. Armadillos are rather fond of over-ripe fruit and earthworms, which can be used to bait them into the traps, although this is always not needed.
Killing armadillos should be a last resort. In Florida, it is lawful for a landowner to humanely dispose of nuisance armadillos.