If you've never removed a radiator before do it in this order, I promise you it's the best way to limit the amount of water spilt;
1. Turn off both valves and place towels under them to catch drips.
2. Get a suitable container (I use an old 2L milk carton with the top on and a hole cut in the other end big enough to fit the radiator inlet into, but a washing up bowl is ok).
3. Slacken the nut. A few drips will come out but that's ok because you have a towel there to catch them.
4. Keep slackening the nut until it's ready to separate from the valve.
5. Get ready to put your dish or container into position; then quickly move the valve and position your dish.
6. Water will start to trickle out. NOW you can open up the bleed valve and control the flow of water (more open lets more air in and empties the rad quicker).
7. If your dish is getting full close the bleed key (doesn't have to be tight) and push the valve back into place while you empty your dish (have a bucket ready). Don't wait until your dish is really full because this makes it more difficult to move quickly.
8. Continue until all the water seems to be out. The more water you empty, the faster you can let it flow. I always lift the rad up at the other end to empty as much as possible.There is usually a bit of play in the pipe, or you can wait until you undo the other valve and then raise it slightly.
9. Radiators can be heavy, so get help if necessary. Lift the rad off and turn it upside down immediately so the valves can't drip the black sludge as you take it out of the way.
10. If the valves are thermostatic valves I'm sure you need to cap these temporarily while the rad is off.