They literally drill a hole into the ground and stick a nuke in it. The surrounding rock is vaporized, but eventually the pressure and heat is low enough that the surrounding earth can contain it. You're left with either a big void in the earth, or if the nuke wasn't buried deep enough the void collapses and makes a crater on the surface.

You might have thought that there was some giant underground complex, but it's really just mining equipment drilling a hole and a bunch of sensors strung out feeding data to recording devices that are a long way away.

https://en.wikipedia.org/wiki/Underground_nuclear_weapons_te...

Edit: to clarify, they don't reuse holes for repeat testing (that I'm aware of), they just drill a new one a few miles apart. So a "testing site" is just a bunch of land that the government owns and is willing to never use it for anything else.