I've been:
Take bore brush, dipped in Hoppe's #9, run through barrel and each chamber.
Clean other parts with toothbrush dipped in Hoppe's.
Take patch/cloth and run in through barrel/each chamber.
Wipe gun down.
Wet the bore to soak.
Remove the crane/cylinder assembly and submerge in solvent.
Take a brush and clean around the forcing cone.
Scrub and dry the bore.
Wipe down the frame with solvent.
Scrub and dry the cylinder (chambers and under the extractor) then reinstall.
Rub a light coat of oil on the entire handgun (bore and cylinders included).
Rule #1 when cleaning - Ammo is either in another room or completely away from the cleaning area! No excuses for I was cleaning it and it went off!
Don't use a lead-away cloth on blued guns until you test it in an inconspicous area first. Some have said it'll remove the bluing.
Look up a diaper service in your area and buy a 5# bag of the old ones for rags. These make great wipedown and polishing cloths. Use one for wiping off the solvent and another for wiping off oil. Wash with detergent or Simple Green(TM) in hot water.
Retain those small plastic trays you find in frozen dinners or side dishes. Clean them out and use them to hold small parts - or dirty patches- while you clean. The ones from the Hormel(TM) entries like Meatloaf and Roast beef are great for soaking slides and small parts. So far I haven't seen the plastic bothered by Hoppe's. This keeps solvents from soaking through to the table or desktop. You might try the ZipLoc disposable "tupperware" containers too.
The rope-style "Bore-Snakes" work! But you do get lead and solvent all over your hands too.
I've never tried wearing latex or Latril gloves when using firearms solvents but it's not a bad idea to prevent exposure to lead and chemicals. But then, most of the chemicals don't seem to bother my hands either.