For transporting fish:
I use a bucket with a lid (I use 7gallon and 2.5gal buckets depending on the size and/or quantity of fish) Home depot and Lowes sells both sizes at a resonable price.
Line the buckets with a heavy duty garbage bag. I use landscapers bags as they are a bit stronger and resist holes fro fin rays and biting fish. You line the buckets because some fish will run rings around the bucket scatching up their eyes, fins and scales. The bags reduce that greatly.
Fill the bucket Half way with tank water, ad the fish, and put the lid on tightly. some people poke holes in the lid and some add battery powered air pumps. I myself do not poke holes for short trips as id prefer to keep in as much heat as I could when I do not have heat packs(which you should use on long trips)
When you get home open the lid and start adding water from YOUR tanks or tank they are going into, into the buckets to accliment them to the water type and temp. I usually add water every 5 minutes until the bucket is full.
ASSUMING YOU KNOW THE FOLLOWING EQUIPMENT IS CLEAN AND HAS NO MEDS OR SICKNESSES IN THE TANK RECENTLY.
Transporting tank:
Empty it. Unless its REALLY dirty dont scrub it clean. leave it alone.
Transporting gravel:
Again with those buckets. I fill them up half way with gravel and them add water from the tank so it just covers the gravel to keep it wet and warm.
When you get home add the gravel to the tank.
transporting Filters:
with just a basic power filter (ie. AC or Emperor) I just empty them out, again rinse them with tank water. Same for sponges, rinse them out with tank water. Filter pads like in the emperors I throw out and replace with new ones. put on the tank and pre-fill with YOUR tank water.
Now with tank in place, gravel in, and filters setup. Fill the tank with new water as close to the temp of the water IN YOUR BUCKETS as you can. Put in your heater in and turn it on. give it time to get the tank up the the temperature of the water IN YOUR BUCKETS.
Add fish and slowly increase the heater temp until it where you want it over the next few hours.
Give it a week or two and do a good gravel cleaning and water change and hopefully you will only have to go through a small cycle if any at all.