In reply to Flinticus:
all depends on how scaled up your valves are. As other have said, my order of preference would be :
1) Don't remove it at all and try to decorate what can be seen. If this is good enough, happy days. Radiator water is filthy dirty and stains anything it touches, so if you can avoid going near it all the better.
2) Drain the whole system down from your drain point and a hosepipe, and just take them off and get the work done quickly before you need heating and/or water again
3) Remove whilst keeping the system live. If you have a thermostatic valve you generally need a special (i.e. came with the valve when new, but now in the bin) cap - you remove the thermostat cap which generally hand unscrew - no need to drain anything - and then screw on this special cap . All the cap does is keep the pin pushed down so that the valve is always closed. For the other end, pull of the plastic cap and either use pliers or a cap with a slot in to close the valve fully.
You then need some thick plastic or freezer bags, two receptacles smaller than the radiator is high, and a bleed key and elastic bands or hair bands. And two people ideally. And some expendable towels, and more plastic for the floor.
Bleed the pressure off then close the bleed screw. With a kind of home made funnel made from the thick plastic underneath, aiming for the receptacle, unscrew the nut on the radiator, when it's off you should be able to pull the leg away from the rad which will mean that the water or black goo will start to come out. It won't come out easily, but in spurts as there is nowhere for the air to get in (think of turning a thin necked bottle of water upside down and how it comes out). I then try to get some thick plastic between the valve and the radiator to try and direct the flow of water, then with your third arm or second person open the bleed screw at the top which means that the flow of water should become more even as the air has a way in. Then your helper can swap the receptacles and rush back and forwards whilst you try and minimise the water getting to places that it shouldn't. Eventually, if both values have been shut off then the water should slow and stop. Try and get your helper to tip the rad to get as much out as you can. Then put plastic or freezer bags over both the rad end and the valve end, to keep crap getting in and and any splashes getting out. Then take off the other end - in theory nothing will come out but it always does, bag both parts and lift the rad off - again easier with two people. And try and avoid kicking or treading on the legs that are left whilst you redecorate. Refitting is slightly easier, as long as nothing leaks.
4) Personally I have done the "loosen the nuts and lie it down whilst still connected" trick before, but wouldn't again. Don't underestimate how heavy a rad full of water is and how much weight it's going to put on the pipe ends that will be propping it up. It scared the life out of me.