If, like GShipley, the new tank is in a different place than the old tank, that's the best and easiest way to do it. Get the new tank up and going for at least 10 days while leaving the old one running as you carefully move LS and LR over. There is no reason why the filtration system should even lose a beat, if you do it right.
If, on the other hand, the new tank is going in the same spot as the old, Dion and Shane H gave some good tips.
Consider and make plans on how to keep things living and aerated in between tanks. Move LR in water not letting it touch the air if possible. When air enters the pores of LR it suffocates and kills the bacteria and small creatures living there. LR has to cycle again if it's got dead things in it.
The temperature can drop to +65 without causing problems so don't worry about a heater, but definitely use powerheads or bubblers for aeration if the stuff is to be in tubs for more than a couple hours.
Keep in mind that LR and LS are as important, if not more important than any coral or fish. They are the lifeblood of the reef tank. If you take good care of the LS and the LR you will have a successful move.
Oh and having plenty of extra saltwater ready and using lots of macroalgae and lighting it 24/7 for while is an excellent way to cover filtration blips. 
Edited by Mark Peterson