About 30 minutes before you're set to leave put him in his container, which should be something like a small box with a dowel stuck straight through and maybe a towel on the bottom if you want. Close it up securely and put it in a quiet spot until you leave. He'll probably hunker down for the "night" and stay either completely asleep or at least calm the entire time. And then when you get to your new home leave him in a quiet spot again while you unload and set up his cage. Once that's up you can let him out and let him settle in.
But all animals suffer far less stress when they can't see and are in the dark, so it's better for them to stay in a little dark box during the move. Some people move them in a small screen cage but I think dark and enclosed is better, in my opinion.