Armadillos are almost blind and are fairly easy to catch. When one is spotted walking leisurely around the yard stopping to nibble every now and then, you must sneak up behind it very quietly (impossible to do in the fall with crispy leaves on the ground) and grab the middle of its tail with a very solid grip and lift it up immediately. It will give a very hard jump when grabbed so you must hold it firmly. Do not let its front feet hit the ground because it can dig so fast and then latch on to the inside of the hole so tightly that you will be unable to pull it out.
They were very common at a large horse barn that I rented a stall at to keep my horse in years ago and I used to catch them, paint racing stripes and numbers on them and release them. This practice ended when I found out that one of the other tenants whipped his little boy for telling such a far out tale of seeing an armadillo that was red and blue and had the number 66 on its side.