Ive also soaked it in warm water (warm...i say again, not HOT) and use a non detergent soap on it to remove dirt. then i treat it with "Linespeed" --made by Scientific Angler, i think---or some other similiar treatment. i like to clean it with warm water first, as i found when i just treated it in the past i sometimes ground dirt into the line instead of cleaning it off...which will make it sink a lot faster and not shoot as well through your guides. soaking it in warm water for 20 or 30 minutes will loosen alot of the dirt and cleaning it will be alot easier.
also---avoid stepping on your lines while fishing, too...this will grind it dirt faster than anything else. i know this, im guilty of it every time i go fishing i think....im hard on my gear.
I run mine through a rag with a mild soap and warm water as Rottal suggested above. Dry it, apply Glide Line Dressing and buff once dry....keeps your line shooting nice and fast. Once every 6 days on the river if you're fanatical or hard on your gear ;-) (me too)....once or twice a year is usually just fine.