Leftover water is the single biggest problem with moving a coffee maker, since it can leak, mold, or freeze in transit. Drain and dry it fully and the rest is a simple wrap and box.
Pro tip: Run a vinegar and water descaling cycle before the move so the machine arrives clean and ready to use on day one in the new kitchen.
Watch out: Never pack a coffee maker with standing water still in the reservoir; it can leak into the box or freeze and crack the tank in a cold truck.