Providing you aren't altering any pipework, you should be able to drain just the radiator you are removing.
Close the valves either end of the radiator (or fit decorators cap on thermostatic valve). note down how many turns (and fractions of a turn) it takes to close the lockshield valve.
Place paint tray or dustpan under one valve to catch the water, loosen the union nut between the valve and the radiator and release the bleed screw.
If more than a couple of bucket fulls of water comes out, a valve is probably leaking. Follow Kevplumb's method to drain the system.
When water stops flowing, loosen the other union, expecting just a few drops of water. Remove radiator but beware of sludge in the bottom of the rad. - once spilt, it's impossible to get it out of carpets - a couple of corks may be useful.
To reconnect, fit and tighten the unions, turn on the valves and bleed the rad.
For a sealed system, re-pressurise and bleed again until rad. is full of water.