I do it this way,
Assuming the old setup is a standard gravel rock arrangement and the new setup is brand new, empty tank. If you dont have rocks or gravel it's that much easier.
1. Put the majority of the old aquarium water in the new tank. 30 to 55 gallons is a bit of a jump, use more than 50% to minimize stress unless your tap water is the same as your old aquarium water (see step 5) or you can make it the same
2. put the fish in a rubbermaid container or something, heat and oxygenate if necessary (reccomended). If your fish are to remain in said bucket for more than say 30 minutes, change the water or add bag buddies (or equivalent hypnotic). however the next steps shouldn't take more than 10-15 minutes
3. take the decor out and put it in a bucket.
4. put the gravel in the new tank.
5. put the decorations in the new tank.
6. refill the new tank. dechlor and add additives just like you would do if you were normally doing a large waterchange
7. put the fish in the new tank. their temperature and water chemistry will be exactly the same (see step 1) so acclimation is unnecessary and would add extra stress for nothing.
8. reinstall filters heaters etc. I would not clean any filter media at this point. clean it in 2 weeks. this is to help reduce any re-cycling spikes etc (highly unlikely).
9. plug in and enjoy your fish. they will take a few hours to reterritorize.