Chain cleaning is as subjective as oil/oil filter threads. But, you asked . . .
Most everyone on the Suzuki V-Strom forum that I frequent uses kerosene and a plastic-bristled brush (toothbrush or the like). I put a little bit of kero in a cup, dip the brush in it, then brush a short section of chain at a time, catching any spillage in a modified drywall mud pan held below the chain. Rotate the tire to a new section of chain, and repeat until the entire chain has been scrubbed.
After cleaning, I use some paper towels to wipe down the chain thoroughly,then I lube it with Dupont Teflon MultiSpray that can be found at Lowe's for a good price. Lubing the chain is also very subjective . . . I used to use 90 weight gear oil, but didn't like the mess, so I changed to the Dupont Teflon Spray. Others use 90 wt., chainsaw bar oil, various bike brands of spray-on lubes, etc. Using WD-40 as a cleaner is a touchy subject . . . some swear it's bad for o-rings, some swear it's totally harmless. Your call . . .
I clean and lube every 600-800 miles, and lube only every 300-400 miles. Lubing immediately after you ride allows the lube to flow into the warm chain's nooks and crannies more efficiently than when the chain's cold, but it's not that big a deal to lube it right after a full-fledged cleaning, either (remember to wipe it down as best you can before lubing). You don't need to make a special run to warm up the chain, just lube it after cleaning, and then lube it again in another 300 miles. You'll be fine.
Some definite don'ts . . . don't use gasoline to clean (that WILL harm the o-rings). Don't use a wire bristled brush on the rollers (use wire on the sideplates only to get rid of any minor surface rust that may appear from time to time . . . plastic on the rollers, wire on the sideplates, if desired).
Chain maintenance is like any other maintenance - you reap what you sow. Don't do it regularly, and you'll be replacing the chain and sprockets much sooner than you would otherwise.
Forgot to mention . . . chain tension is also a key factor to chain performance and longevity. Read your owner's manual to find out the recommended tension, and try to stick with it. Tension on the loose end of the range is better than too tight . . . a tight chain will accelerate the wear on the sprocket teeth, and necessitate early replacement. Obviously, you don't want a chain that's TOO loose, either . . . when they come off the sprockets at speed, bad things happen.
That's about it. Hope this helps you out.