I have moved tanks a few times.What I find works best is:
I recommmend doing this on water change day...too keep things as normal as possible.
Take out a bit more than half of your water and put it into a clean bucket.Now remove all of your decorations and/or plants,try not to stir up the gravel to much,maybe put a few or your decorations in the bucket aswell and then catch all of your fish and put them into the bucket.Take some of the very topmost layer of gravel and put it in the bucket with your saved water and fish,if you have an air pump throw the stone in the water just to keep the water aerated,also remember to keep your filter wet and aerated if you will have it out of water very long.Now suck out the rest of the water into a different bucket vacuming all the while to get as much stuff out as possible.Now that all your water is gone it's a good time to give your remaining gravel a good rinse.I use a noddle strainer and rinse it a strainer full at a time,when rinsed put in right into the new tank.Now add some of your (saved) water and then replant and put in your decorations back in,add a gallon or 2 more of new water and then the fish,finish off filling it with the rest of your saved water,get your filter in and take the little bit of saved (unwashed) gravel and spread it around the tank.top off the water and your done. I always add a doseing of stress zyme when finished.
Like i said i've done this a few times and never lost a fish.......