So armadillos leave two different kinds of dig marks in my experience. Out in the open lawn areas they tend to leave shallow dig marks about 1-3 inches wide and deep. Around flower beds with very rich soil and lots of worms, I've seen them dig holes as wide as their bodies and about a foot deep.
We lived in the city limits (so shooting them wasn't an option) when I learned to trap them. We borrowed a live trap from someone we knew, and didn't even use bait. All we did was set the trap in the yard, with a couple of 2x4s (or 2x6s would work) in a V shape leading into the trap. The armadillos move along with their noses to the ground sniffing for bugs. When they come to the boards (standing on end like little walls), they just keep sniffing along the boards until they walk right into the traps.
We caught several of them that way. We just drove them out of town a ways and turned them loose. (There's probably some rancher who hated us for it though)
You may also find that you can walk outside at night with a light and find them walking around your yard....We may have dispatched one or two armadillos with blunt force trauma when we spotted them outside the trap. I don't recommend that method as I don't like to kill anything I don't need to, but it worked as well.