Nature's provided you with a base and support - just cover the flattened base pads with about 1/2" of soil and away they'll go in the spring, although there will be some growth year-around if the weather is warmish and there's some water and sun. Opuntias (the genus of cactus you have) have species that grow from the Peace River in northern British Columbia all the way down the Americas to Tierra del Fuego - they're easily one of the most opportunistic, as your picture aptly shows, members of the Cactus Family.

Or don't cover it with dirt - your Opuntia will grow anyway, just not as quickly / lushly as that of one planted.

Much appreciated, cactusmcharris. It's very true, just keeping this little guy in a small amount of water in a bowl has kept it thriving.

A related question, what kind of gloves are best for transplanting cacti?

Opuntias, as well as having spines, have glochids, which aren't particularly painful, but they're intensely irritating and numerous. Any pair of gloves that I've used to move Opuntias got the glochids stuck in them, rendering them full of nearly-invisible stickers, and I usually throw them away.....so what I'm saying is use sheets of newspaper or the like, and fold them so you can grasp the pad indirectly with a strap of newspaper. Old carpet also works.

when it comes to Opuntias, I recommend NOT using gloves- false sense of security. As recommended above, paper or carpet work great, as do cotton sheets, blankets, etc. Nothing more frustrating than using gloves, then picking them a few weeks later and getting all t he glochids that were adhered to the gloves in your skin. Best just to not touch Opuntias with any gloves you ever plan to use again (Home depot has $1.50 gloves, so if I DO happen to screw up and get them covered with glochids, in the trash they go).

Get yourself a dedicated set of tongs for the garden

Yes, the gloves I used did get the glochids stuck in then, and I got stuck anyway. Thank you all for the suggestions! I have a set of tongs I think would be perfect for this.

Elmer's White Glue is handy when your hands have infestations of them.

That's brilliant, cactusmcharris! Thank you, I will be getting Elmer's next time I go shopping.