Barely insert the arm into free-draining soil, support it with rocks, and stand back as it takes over. Seriously, they can just lay on the ground and they'll root, but you'll give it a head start by making it vertical. Mist it every few days and, given warm temps and sunny days, you'll likely have roots within two weeks.

I'm glad to see that you have it under some control in a pot - I daresay if that beast was let loose in the ground you'd have a impenetrable botanical berm in no time.

It's an Opuntia (of the Cylindropuntia subtribe) but I don't know the species.

It does not spread too quickly here in Central Texas. Cylindropuntia leptocaulis will. Or that has been my experience sittin in Caliche and Limestone rubble. Most of my cylindropuntias grow tall and then branch.