I do as was mentioned earlier. But when removing the cover bolts I LOOSEN THEM, not taking them all the way out. That way you can get a scraper in the bottom and pry it open a little for drainage so you don't end up with a big mess.
Also while cleaning out the gunk that's usually inside of the differential use a cloth rag, not paper towel. I left a small piece of toweling behind one time that got sucked up into the suction tube. That was a mistake I did one time, and one time only.
I had everything changed, went to till a food plot, got done and on my way home the tractor stopped dead in it's tracks. For the life of me I couldn't think what would have happened. Got it back to the shop, drained all the fluid back out got to looking with a flash light... there was a piece of toweling. Lesson learned.