The way I do it is: -
Tighten down the lockshield valves on both ends. One of these is normally the adjustable one to turn the rad on/off (or TRV if fitted), the other one is the balancing lockshield.
Put old cloth or newspaper on carpet under one end, then old square icecream tub - just a convenient size to fit under and holds a fair amount of water.
Loosen the horizontal nut between the lockshield and the rad - probably stiff - and ensure water trickles into tub.
Open the air bleed above to increase flow of water out the bottom. Empty the rad of water.
Unscrew other end and raise this end slightly. Rest of water pours into tub - often with black sludge (avoid getting on carpet at all costs).
When empty of water/sludge, lift rad vertically off its two brackets at the back.
Job done.