Wear gloves for this. I tried it without gloves once and ended up with a bunch of spines and splinters. They're really fine and a pain to get out.
I buried each one just deep enough that the dirt was level, with room left to put rocks back on top. Good drainage matters a lot here so you don't get rot in the cactus.
The first one was pretty easy. The second one was tough. The roots were growing through the pot, so I had to cut the pot off. I wasn't as careful with that one and broke off a good pad, which sucks. I'll replant it somewhere else.
It had just rained, so the ground was soft and the pads were nice and plump. That made it a good time for this kind of job.
I've been tossing the extra nopales (prickly pear pads) along the side of the yard. I wasn't trying to plant them, but they rooted anyway. I've been told not to plant them that way, but it's working. The roots are growing into the ground in a really dry spot, and I haven't been watering them at all. I cleaned up the weeds there and threw a few more pads down so they keep growing.
From here, I'll eat some and plant some, and the wall of cactus will keep filling in. I'm treating it like a little experiment. I might leave some just lying there to see if they take, and plant others half in the ground, half out, like I did before.
If you want to plant one properly, give the cut end some time first. I keep a pad in a pot for three or four days until the cut starts to close and roots start coming out. Then it can go in the ground about halfway up. I might do a separate video on that if you're interested.
Grass tends to grow over that area after heavy rains, so I went back with a propane torch to clear it out along with the leaves and other debris. Keep a garden hose ready, especially if you're working next to a fence like I was. After that I hit the area with water to clean up the rocks. Those are river rocks I got from Home Depot.
I use that torch for pretty much everything now, including starting charcoal.