Two ways that I've used.
One, assuming it's a quick move: Bag the animals and plants. Take the water out of the tanks (I carried much of the water in several 5 gal buckets to ease the restart of the tanks.
The other is to drain all but a couple of inches of water out of the tanks and move them that way. You are more likely to develop leaks with this method, or at least that was my experience. I saved the water I drained out and replaced it when I got there.
It all depends on how your are moving (vehicles, professional movers, etc.). Or you can use a mixture of the above. Good luck.
Bob