well usually you have to take the system apart to clean. if it's an all in one water cooler, then you just blow compressed air through the radiator.
if it is a custom system, then you just need to flush the loop (run water through it with it draining into your sink or something) for other parts, you literally can wash them, then dry them with a hairdryer, but this isnt really necessary or advised (usually only pro modders do it for photo shoots) just compressed air the crap outa it, get into every nook and cranny, then just sweep it off your floor after.