A special glass cup is rubbed with a flammable liquid (most often rubbing alcohol, I use 70%) and lit with a torch, which can be anything from a BBQ lighter to a specially made torch with a cotton end. Immediately after lighting it, it is placed on the skin and the flame inside goes out and creates a vacuum pulling the skin up.
I've been firecupped a bunch of times and I've done it, too. It feels really, really good. The cups can be on very tight or loose. If you add baby oil or lubricant, you can move the cups around, which feels good too. It leaves red or purple marks for up to a week. It's great for loosening muscles.
My friend got kicked by a horse, so we firecupped her. It's painless. It feels good. She felt much better after. I find it very relaxing. Here are some pics.
Warming up with light "fire play". Running a flame along the back and putting it out.
Putting on some small firecups.
You can see the skin tightening up here.
A back full of firecups and Chinese suction cups which work in a similar manner, just without fire.
The resulting marks are slightly raised and go away quickly. The big bruise at the bottom side is from the horse kick.