I toss the chain into a bucket of warm water with Simple Green pro HD cleaner mixed in. It goes in with all the other components and sits for a handful of hours.
I'll stir the bucket a few times to sluff off the grime that's loose so the following layers of crud can begin to loosen.

Then I rinse the chain under water and use annylon brush to scrub each side. Rinse the chain and pull it thru a towel to both dry and get any remaining grease or dirt off.


At that point I can see if thew is rust or not. Rusty chains are tossed.
I hang the chain up until it's time to reattach.

I lube it with some dry chain oil.

Pretty basic, I treat the chain like the derailleurs and everything else that is in working order and just dirty- degrease, scrub, dry.