I like to get the bike up on a rear stand and spray the chain down with WD40, scrub with a toothbrush (not your current one but feel free if you want to

) and then follow with more WD and paper towels to wick away the dirty stuff. Use paper towels until very little residue from the WD comes off and then spray on a good quality grease based chain lube like Silkolene or PJ1. Stay away from the wax based lubes. They attract less crud but they don't protect from rust worth a damn.
And don't forget to brush away at the lube buildup on the side of the rear sprocket and in the teeth.
To help keep the tire, wheel and the rest of the bike clean during all this splashing around I made up a corrugated plastic guard that fits up between the wheel and the swingarm and circles quite closely around the wheel hub between the rear sprocket and the spokes.
And for safety sake be sure you spin the tire so the chain sweeps off the sprocket. Getting a finger caught in there due to spinning it the wrong way will really put a damper on your day. That chain and sprocket with the momentum of the wheel to back it up will act just like a guillotine.