Hi
Ive done a move already and am just about to upgrade again. The best way is to have the 2 tanks set up and running so the new tank has time to stablise Sg PH Temp etc. It will also give you time to weed out any problems with equipment and flow. If your planning to give the new tank time to settle then leave it to do a full cycle before adding anything. But obviously if you are using the same contents, i.e. rock sand and coral, and not ading much new then its a case of half fill the tank with salt water, make sure everything is running fine. Leave overnight is possible to ensure both Sg temp and Ph are stable. Then its buckets and tubs i'm afarid!.. Firstly take out any corals and add to a bucket with water from the tank. Then in a second large tub add most of your rock work with water. Then third bucket with tank water catch your fish, also place in some rock that is sturday and wont tople over to help the fish feel secure. I would make sure the buckets are kept somewhere out of drafts and away from noise and cover with towels while your swapping over sand from the old to the new tank. Before remove the sand you can save the rest of the water if you are using it to top off, but i would stick a filter in the bucket with filter floss in to remove and rubbish.
Now you can start on the new tank. Add 50% of your sand, best done with a plastic beaker or something similar. Slowly lower the full cup to the bottom of the tank the gently poor out the sand and level off. This way it does not make too much mess and will take less time to settle. You can now add your base rock to the sand and do some scaping. Now you can add the remainder of your rock from the bucket and finish your scaping. Now the last of the sand can go in using the same method as before placing it around the rock work to give a little more support.
I would top off most of your water now and give things time to settle and filter you have time to clean up the tank.
Once its pretty clear you can then add the corals either direct to rock work or place on the sand.
Then when you are sure everything is OK the fish can go back in.
I'm not saying this is the perfect way to go and i'm sure others will have bits to add but it worked great for me with no fish or coral deaths what so ever. I turned my tanks around in a few hours and there where no problems. I guess planning is the key. Make sure you have everything to hand before you start, and dont rush! Slow and steady wins the race.
Good luck with it