If you've ever burst a head gasket and have sludge or goo in the cooling system that makes the coolant brown and cloudy, then it's worth flushing it using a proprietary flushing agent. The instructions will be on the flusher.
If your coolant is clear blue (or pink) then you don't need a flusher, since most of the stuff that's in there that shouldn't be, is loose scale etc. rather than goo.. but you can shift some of it at least by flushing the system with just clean water.
Once you have drained the coolant, replace the bottom hose (loosely.. don't fit the clip) and then refill the system with clean water. Run the engine for about 10 seconds to get it pumped round the internals and switch off. Then quickly
pull off the bottom hose so that the water rushes out. This can go all over the floor, so no worries.. it'll drain away.
The force of that water gushing out will pick up any "bits" and carry them out. If you feel you need to repeat the process, repeat the process. You should have more or less completely clean water coming out.
If you're switching from blue anti-freeze to pink, then you should always do this flush with clean water, since the 2 types of anti-freeze are "incompatible" (I'll have to try out what happens when they mix..
If your header is skanky, then take it off and clean the inside. If you let it dry out completely, then paraffin is the best stuff to use to shift any brown stuff.. Rinse it out with water and some toilet cleaner (that removes limescale) or denture cleaner.. You don't get many opportunities to get it all completely clean...
When you're done, re-fit the header tank, re-attach the hoses and tighten it all up (stick a bit of gasket sealant on the clip threads, to stop them unscrewing) and then refill with a 50% anti-freeze and distilled water mix - unless your water is "soft" in which case it'll be okay to use tap water.