My fish sitter has a set of instructions on what to do in case of various emergencies. I have this laminated and tacked to the wall in the fish room.
If you have a person who is coming over to take care of your house/fish, you can leave the same.
First, open all the tank lids to increase oxygen exchange.
Second, pull all media from the filter boxes and drop them into the main tank to stay wet and in contact with the fish waste.
Third, STOP FEEDING.
Fourth, I have the sitter UNPLUG all the filters and lights and UV units, etc. That way, if the power comes back on and the filters are empty, they will not grind and potentially burn out. I leave all air pumps and such plugged in - air is essential.
To protect against short power outages - 6 hours and less, I have purchased the battery backups that are made for computers and other heavy-electrical demand high tech equipment. These are plugged into the wall, and all the "essential" pieces of fish equipment are plugged into them. This means the air pumps, mostly. When the power goes off, these battery backups will keep the air equipment, and usually one small filter going on each tank for about 8 hours. When the power comes back on, they automatically switch back and recharge. They protect when the power does a brownout or partial return - preventing burnout.
Even all these precautions do not always work. I lost 6 VERY VALUABLE Ranchu fry this past spring due to a power outage when I was out of town. I am still kicking myself and crying over those.