The best way is to take the chain off and agitate it in a solvent. Gasoline works great. Do this twice, with fresh solvent the second time. Dry well, install, and lube with chain lube. Not with anything else.
To clean without taking the chain off, spray it well with a strong soap like Simple Green. Let it soak in for a few minutes, and spray off with garden hose. Repeat. Let it dry well and lube.
Don't try and extend the life of your chain too much. You'll end up ruining the cogs. 1/8 inch stretch max. A new chain will measure 1 inch, link to link. 1 and 1/8th, time for new chain. I've read it's best just to change it out after 2000 miles, but who counts?