Hi and welcome to the forum
Don't feed the fish for 24 hours before moving it.
Do a 75% water change and gravel clean the substrate each day for a few days (or a week if possible) before moving. Do not do a water change on the day you move.
Clean the filter a few days before moving.
Then use a bag like Nick suggested or get a large plastic bucket with lid and put the fish and some water in that. If you have a battery operated air pump that can be used to aerate the water on the way home.
If you use a battery operated air pump, do not use the normal sand airstone that comes with it because they put too much back pressure on the pump. Use a plastic multi-coloured airstone or no airstone to create bubbles. You can use a small lead weight like a fishing sinker to hold the airline down.
If you are taking the tank with you, then drain all the water out and remove the gravel. Put the gravel in a separate bucket and discard whatever water you don't use to keep the fish in during the trip home.
Put the filter materials in a bucket of tank water and the filter bacteria should be fine for a few hours.
Wash the filter case and motor under tap water and rinse the tank out. Put the aquarium on a blanket in the car somewhere so it doesn't move around and get damaged. Put the filter, heater, etc into a bucket and put all the stuff in the car and go for a drive.
--------------------------
If you are transporting the fish in a bag of water, get the biggest bag you can (within reason). You want about 1-2 litres (1/4-1/2 gallon) of water, or more if possible. Half fill the bag with water and blow air into the bag so it is full. Then put a rubber band on it to seal it up.
Put the bag with the fish into another bag and seal that up. Then wrap the fish in a towel or blanket and put it in a box or esky to keep the temperature stabile. The fish should be fine like this for several hours.
