Take it off (there should be a separator link) and clean it thoroughly in several changes of paraffin or white spirit or turps subs. Pull it through an old towel then allow it to dry overnight. While that's happening use the paraffin-damped towel to get the dirt off the chainrings, jockey wheels and then the cassette by sitting with the wheel on your lap, cassette uppermost, and pulling the edge of the towel back and forth between the gears with a sawing motion, allowing the cassette to rotate.
Store dirty paraffin in an old jam jar and you'll find that the dirt drops to the bottom leaving clear paraffin, which you can recycle for a long time.
Replace the chain and if you're sure it's dry, re-lube sparingly with a dry wax-based evaporating solvent lubricant like Finish Line. My philosophy is to keep the chain clean and dryish because this is less likely to pick up dust and grit and make everything dirty by contact. The other philosophy is to lubricate the chain frequently with a wet lube and run it through an old towel after every ride to remove the dirt, sometimes called the Mickle Method on here after the person who described it. Either way seems to work fine.
Do not waste your money on a clamp-on chain cleaning bath thingy - they are disastrous because the cleaner will find its way up the "legs" of the chainset and eventually into the BB bearings, washing out all the grease. Don't ask me how I know this.
