Put the fish in a temporary container. Depending on the size and number fish it could be something like a bucket or a very large rubbermaid container. Fill it up with water from your tank. The biggest issue you need to worry is making sure the fish stay oxygenated. The easiest way to do this is with a small air pump.
Once the fish are in a new home drain all the water from the tank. You don't want to transport it with the water. Make sure your filter media stays wet to keep your bacteria alive. If you have a canister filter leave it full of water if you have a HOB filter than submerge the media in tank water. during transport.
On the other side, refill the tank, dechlorinate if needed. If the temp of your tap water is very different from the tank water bring it to the correct temp. Replace the filter media and setup the filter. At this point you should reacclimate the fish as if you were bringing them home from the store.
It should be pretty easy really, just make sure you run the air pump on both sides.
