I've wondered many times how the camera work is achieved when the dancers are spinning one way and the camera is going the other.

The obvious answer is that there is a skilled Steadicam operator on the dance floor wearing silent roller blades and, whenever the director cuts to a wider view, he's careful not to include the floor bound cameraman in the frame.

If that's not how it's done (and I don't really think for a second that it is!) does anybody know how the ground level dance floor shots are achieved?

The camera positions are as closely choreographed as the dance itself; that's what the Friday night and Saturday rehearsals are for. And yes there are times when camera operators wear roller blades! It's usually more pedestrian than that, literally, but there is always at least one cameraman on the floor itself. For the actual broadcast the director will be working from a predetermined script agreed with the cameramen.

Here's how they do it at DWTS

A few years ago, the SCD website showed a fixed camera view of some dances as well as the televised intercut version.
In this you could see the steadicam guy. It was interesting how his movements were planned around the dance

I'd suggest he doesn't have to travel far as the dance floor is much smaller than it seems on TV.

They do a good job, mind.

it's because they feed the cameramen a special diet of titbiscuits, which dopes them to superhuman levels of pointless idiocy.