I find the best way to move them is in bags. Get some fish bags from the LFS, or buy them, fill them 1/3 with water (place one fish per bag unless they're little guys), then seal them in with air. Double bag them for safety, and flipping the inside one upside down will keep small fish from getting crushed in the corners. Throw the bags into a cheap styrofoam cooler (or whatever you have on hand), to keep the temperature stable. Now you can easily set up the tank on the other end and introduce the fish by floating them and pouring them in.
Just like when we bring them home from the pet store or breeder, there's no reason to transport more water with you.
It's best not to feed them for 2 or 3 days before, this way the bags will stay clean.
Hope that helps