I'm not sure if this is the best way or even safe. It is effective though...
When handling carboys, I always work on a layer of thick towels. Never have them directly contact the floor.
When I'm at 5 gallons, I re-sanitize the neck with Starsan and put a sanitized stopper on the carboy. I kneel in front of the carboy, and cradle it sideways on my lap. Then holding the neck clamping the stopper, I shake the carboy sideways with a rocking motion. This aerates and mixes up the wort. After a minute shaking I put it upright, spray Starsan around the stopper, and open it, hopefully to let some more air in. I repeat this 1 more time.