If its really filthy. get an old stocking, double it over and stick it in the upper radiator hose as a 'sock' filter.
Drain the system and fill it with a mixture of roughly half a cup of vinegar to every litre of water. do a couple of runs around the block. Flush as whincup described above. clean your filter. fill with clean water only. go for another half hour or so drive. remove the filter. if you water is still clear flush and change again and add coolant if you use it. If not repeat with the vinegar.
The heavier cleaners can do as much damage as good if not flushed properly. Vinegar is a fairly mild acid and enviromentally friendly compared to most of them
The stocking will break down after a few of days of being there so only use the same piece once, and once your happy it's not catching much more crud remove it, but check often because it can cause a blockage!
Make sure your heater tap is ON.
be carefull pressure hosing the outside of your radiator, you'll bend the fins.