Typically best to get this started off early. First step is to contact your nearest TMO (Travel Management Office). They'll email you a link to an online form that you fill out with a lot of the info for your move (i.e., whether you're doing the entire move yourself, or you're moving some of your stuff but want the movers to take the rest.) I did a partial, and it worked out fine.
You'll want to scout out a scale someplace near your home. Weigh your car before you put all the stuff in, then after. The gov't compensates you by weight moved.