In my
experience, live trapping them is fairly easy.
Ive found that setting an unbaited live trap, then build a "funnel fence" at 45 degree angles from each side of the trap entrance to a length of 8 to 16 feet is the preferences method in my area of Oklahoma.
The funnel
fence only needs to be 6-8 inches tall.
Armadillos tend to like edges and have poor eyesight, so they will eventually find the trap during their forays through the property.
Disposing of the armadillo is a different matter all together.
I personally give the critter a final "swimming lesson" by placinging the whole trap in a
compost tea tank for 30 minutes and then compost the whole carcass afterwards.
As for protecting a garden, I've found the surrounding the garden with a 16 inch welded wire
fence, buried 4 inches in the ground tends to be quite effective.