Two schools of thought – you can get kit that will freeze both connections, and then the rad can be taken out without draining everything. I’ve never used this method though.
Easiest to drain everything out (there should be a drain cock somewhere that a hose pipe will fit onto) and replace from there. In my experience, sludge will sit in the bottom of the radiators and not in the pipes – the only really effective way to clean them out is to turn them on their side in the garden and blast out with a hose, and you really need to do this to all the rads at once to make it worthwhile.
Refill using a pot of corrosion inhibitor mixed in.