It's fairly simple, but you do need to watch getting dirty water on the carpet.
As the pipes enter and exit the radiator you should see they go through valves. You tighten both of these up to avoid further water draining out from the system when the radiator has been taken off.
You then use a spanner to loosen the nuts nearest the radiator. If you are luck you may find enough flexibility in the pipes under the floor to only loosen the nuts and then lift the radiator off it's brackets, and turn it 90º and rest it on something without needing to take it right off. If you can you can then tighten the nuts back up again to prevent water seeping out.
If this doesn't prove possible then you continue to unscrew the nuts until you can pull the pipes away from the radiator. It is during this time water will drain out of the radiator so keep a bowl under each inlet/outlet. Preferably remove or cover the carpet. Make sure you bowl is large enough so you can tip the radiator and drain all the water out. Then put the radiator somewhere where any further seepage of dirty water won't be a problem.
Remove brackets from wall, do whatever you want to do to the wall, then reverse the procedure to put it all back.