WD-40 and a shop rag. Spray, wipe clean. Re-apply the lube.
Keeping a chain clean won't necessarily increase the chain's life, but it will keep it shifting well. A dirty chain loses it's lateral flex; at best you'll experience poor shifting, at worst, you'll drop the chain when you are out of the saddle and shifting to sprint... (Ask me how I know that
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Get a chain stretch gauge and replace it when it it out of spec. Running a stretched chain will chew up the rear cassette, and you'll wind up replacing both. My 11 speed chains run about $45-50 and replacing my Ultegra 11 speed cassette would cost about $80+, excluding labor.
By the way, your weight and power will factor into the chain life more than anything else. Some of the smaller guys I ride with can go close to 10k on one chain. I'm 220 lbs and put down lots of watts, and I only get 1500 - 2000 miles before it stretches too much.