If you need to move your goldfish and it will take you more than an hour or two to reach the new location, the key idea is to fast them. The killer for goldfish is the build up of ammonia in the water they are transported in. For shipping this is particularly egregious, since the fish are typically in the minimum amount of water possible (for weight and air volume considerations).
Fasting for a week is not unreasonable. Al Foster has also recommended a one-week fast for fish you intend to show, since show tanks typically have the ammonia controlled by water changes. I ran an experiment where I tested a fish that had been fasted for four days against some normally fed fish. The result was that the fasted fishs ammonia output was less than one half the normal output.
If you are driving your fish to a new location, you have the luxury of using larger containers. My favorites are 5-gallon buckets. I fill these half full and then put plastic with a few holes in it over the top (to limit sloshing out of the bucket). In a pinch, you can keep 4 fasted 3 inch fish in this for 8 hours. Though more space is better, if you can offer it.
When you reach your destination, if the pH of the new water is within 0.2 of the old pH (hopefully you have anticipated this and have made sure this is the case by "pre-adapting" your fish), then the next step is to fill a bucket with dechlorinated fresh water of the same temperature as the transport buckets. Then I would lift the fish out of the old water and place them into the fresh water. Then use this bucket to temperature equalize the fish for the tank they will go into. This gets them out of the ammonia right away, but lets you spend time equalizing the temperatures.
There are two other things you also need to be careful about when transporting goldfish: temperature fluctuations and physical trauma. For the temperature, you want to keep it as consistent as you can. Using a large volume of water and placing it in an insulated container will help. To avoid physical damage to the fish you need to keep anything abrasive, sharp, or otherwise potentially dangerous out of the transportation container. If you are moving the fish in plastic bags, be sure that the bags do not have folds that the fish will swim into and get stuck in, particularly if the bags can shift while the vehicle is moving.
If your move will take multiple days (e.g. across the US), then you have a challenge ahead of you. I dont really have any great suggestions. You might bring an extra bucket and an assortment of water conditioners and a buffer to whatever pH you are at. You could then fill the bucket when you stop for the night, treat the water (and buffer it, if needed, but careful of pH bounce!). And then let the water sit overnight and use it to change the fish water in the morning.
One last thing: ammonia becomes more toxic the higher the pH of the water. The goldfish will be much less damaged by ammonia at a pH of 6.8 than at a pH of 8.5. Keep this in mind as a caution and try to avoid any significant exposure to ammonia at higher pHs.