When I first started having issues with armadillos wreaking havoc in our flowerbeds, I baited a couple traps as I was told by FIL and caught a couple of raccoons. Then I researched and found out about the funneling method where you have a barrier that guides them into the trap as mentioned above. I got some of this silt fencing at Home Depot and made a funnel of it in the yard. It works but you have the inconvenience of having that barrier in the way of mowing, walking around the lawn, etc.
Then I just bought some sub-sonic .22 LR rounds and started shooting them. Of course that means getting outside at odd hours of the night to catch them in the act. But since I fenced the back yard they don't come around much anymore.