For starters: Lots of patience and time to reserve for that matter
As Twistermom said, organize plenty of buckets with lids (make sure they had no chemicals in it prior to fish use) catch and place all your fish in there.
If you're dealing with a big tank (eg 55g or larger) it helps to drain half the tank water prior to the fish-catching action.
Reason you want to keep filter & gravel wet during the move: So your beneficial bacteria doesn't die on you
Its also helpful to have your car pre-heated when transporting all of this, to avoid a heavy Temp shock for the fish (unless you live down south).
At the new place either use the old water (if tap is different then the old parameters) set up & fill up the tank quick and acclimate the fish to it and re-place them in their new old home.
Make sure to hook up the filter asap when you have water running in the tank to avoid delay's there that could poss. harm the bacteria.
All that said, what's also a good & safe way to transport the fish in rough climates (winter time) wrap the buckets in bubble rap as they'll create these warm air pockets around the buckets.
On all this action you want to move quick, not like pack it all up, let it sit for day or two and then set it up, this action should be pulled off start to finish in one go so reserve plenty time for it (I'd suggest 1 moving day just for this).