Normally they just turn the gas off at the meter, out the front of the house, or get the company to turn it off somewhere before the house. Then they undo a couple of nuts and remove the meter, replace it with a new one and do the nuts back up.
If the gas pipes in the house are damaged, they might need to use an oxy acetylene torch (welding) to cut through the pipe, replace the meter and then more oxy to weld the pipe back together. However, if the pipes are in good condition (and they usually are), it's just undo nuts and swap the meter, no welding involved.
If they use an oxy torch, you will need to open the windows and get some air flowing through the room. Turn any air pumps off while they are working in there, and try to cover all tanks and ponds with paper or plastic to stop any fumes potentially getting into the water. There shouldn't be any problems because the smoke from the oxy torch rises and there shouldn't be much smoke, but it's always a good idea to cover tanks when there is smoke or fumes in the room.
They might ask for all power points to be turned off while working with the gas. This is to prevent an explosion if there is a gas leak. The fish will be fine without power for the time it takes to swap the meter over (about half an hour). If you can clear the area around the gas meter before the repair guy comes, it will make it easier for him and he should be there for less time.