Soaking a chain in solvent can be useful if it has a lot of thick, hardened gunk on it. From there, you need to articulate the chain somehow so that the loosened grit can find its way out. Shaking it in a jar will do a lot, ultrasonic cleaners can also be good for vibrating out the grit. (I'll often do both -- shake the jar for a few seconds between passes in the ultrasonic cleaner.)

I'll add my voice to those saying just to air-dry once you're done. Water just invites rust when on clean metal, so rain is the only source of water I'll (begrudgingly) permit to touch my chain.