Set the new tank up, fill it with dechlorinated water. Let it run for a few days then scoop the fish out of the old tank and put them in the new tank. Move the filter into the new tank and your done.
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If the new tank is going where the old tank is, put the fish into a large bucket or plastic storage container with water from the original tank. Try to keep as much of the old water as possible. Have an airstone bubbling away in the container. Put a lid on the container to stop the fish jumping out.
Then clean the filter in old tank water and put the cleaned filter media in the bucket with the fish or a separate bucket of tank water. You can also clean the filter a day or two before moving the fish and this means you don't have to do it on the day of the move.
Empty the old tank. Move it out of the way. Put the new tank in place. Set the new tank up and fill it with as much old water as you can. If there is more than 4 inches of old water in the new tank, add the fish too. Then top up with dechlorinated water. Add the plants and filter to the new tank. Turn filter on and your done.
Don't feed the fish until the following day.