The substrate is always the hardest bit to move. Don't feed your fish for 24 hours before the move. This will reduce waste in the temporary buckets.
Firstly syphon clean tank water into larger container, usually a bucket. Add fish and shrimp and a few plants (real or plastic), filter if it fits, heater stat, air stone if you have it and DONT feed the fish. Cover with a dark towel or sheet, fish stress less in the dark.
Remove and save any extra tank water leaving about a third in the old tank. Give the substrate a good old turn over releasing all the grunge into the water. Let it settle and syphon out the dirty water whilst gravel cleaning the substrate surface.
Transport your old gravel to the new tank. Add a couple of gallons of conditions tap water and stir it up again and syphon off debris. If you intend to add more substrate then layer that on top.
Add your tank decor and fill with and clean left over water from your old tank and top up with conditioned tap water. Install the heater/stat and filter. Get them all going.
The tank will be cloudy for a few days and it may mean cleaning the filters a LITTLE to help reduce cloudiness, it will soon settle.
Once the tank is up to temp and filters running normally introduce your fish and shrimp as if you've just got them home from the LFS, using which ever acclimatisation method you prefer.
Do check water parameters daily until you are confident the cycling has not been affected and WC as required. Do not over feed fish to settle them in, quite the opposite, add minute amounts of food. If they don't devour it then wait a day. Uneaten food at this stage can cause massive ammonia spikes.
I hope that's clear and of some help. Good luck.
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