I've done this literally tens of times. This is how I go about it:
Scenario #1, old tank to new tank with NEW filter on NEW tank
1) Put the fish in buckets or wherever you keep them for the interim period between placing them in the new tank.
2) Add substrate and decorations for new tank (if not using old substrate established with bacteria, substrate from old tank then go to #4 right quick).
3) Match new water for new tank with temperature of old water from old tank while filling new, larger tank. Dechlorinatorrrrr!
4) Run, or place in tank somewhere, old established filter media from old established filter. Yes, I use the word established a ton. It is extremely important. If using a new filter or new substrate this is vital for the health of your fish because bb does not live in mass quantities in the water itself. Leave the old media in the tank and check levels and parameters daily. I leave it in there for around a week just to be safe because I have incredible ocd regarding my fish.
Scenario # 2, old tank to new tank with OLD established filter
Just do the move...if you are adding a new filter with new filter media or new substrate then I would fast the fish for two nights and a day before the move, then the same for the period after, as he said. This well help in not overpowering your new filtration. Adding fish slowly can help too, I suppose, but AIN'T NOBODY GOT TIME FO' THAT!!! Had to...sorry...
Jeeze...I think that's it.
:cheers: