Do a leak test a day or two in advance.
I would have several buckets or lined styrofoam containers standing by.
I'd drain the water into a large vessel (45 gallon rubbermaid trashcan) and as the corals become exposed move them into buckets. Move the LR into separate buckets or another large vessel. Be sure to drain a large portion of the water before you stir anything up.
Once you empty the tank (assuming that the new one is replacing it) get it out of the way and get the new one in place and start filling the new tank.
Have a bucket of reefwater that you can rinse the detritus of each piece of rock as you place it into the new tank.
Place your corals and slowly add any new saltwater (having premixed and aged about 250G is key)
Float your fish in bags before re-introducing them as if they were coming from the store.
There's really no fool proof way to do it, but you'd better have a really good idea of how the new system will be plumbed before you do this or you'll be running back and forth to the Home Depot and loosing valuable time.
I would prefer to do this in steps over a few days or a week or you may loose some livestock. This will be like doing an 80% water change. If you have the ability to store your livestock in the current system while your new one is being set up in a remote location I would do it. If the new tank is going in the old tank's location, I'd set up a few large containers like maybe two 100G Rubbermaid horse troughs to house your current livestock while the new system is set up.
Good luck!