The really short answer: DO NOTHING. Or, more precisely, do not keep opening your fridge or freezer. The longer your fridge or freezer door stays closed, the better the chance that the items inside will remain cold.
Food that is in a freezer that remains unopened, is full, is in a cool place, and is well insulated, will stay cold for 2-4 days. Since not all freezers are in cool places and are well insulated, you can expect a full, closed freezer to remain cold for up to 2 days.
If the power goes out for an extended time and your food thaws, you can safely refreeze the food if it contains ice crystals and is still cold (about 40F). The quality will be lower, but it will be safe to eat.
If the food has been above 40F for 6 hours or more, keep only fruits and fruit juices, breads, cakes, cookies, flour, nuts and hard cheese (but absolutely discard these items if they show any signs of spoilage).
If food has been above 40F for more than 2 hours, discard milk and milk products (except for butter and hard cheese); cooked eggs and egg products such as custards and puddings; cooked vegetables, meats, pastas, and salads containing these items; and all other perishable items.
Before Using Foods That Have Thawed
Check your food for off colors or odors. Bacteria can multiply quickly, and most bacteria are odorless and colorless. The mantra we repeat in Master Food Preservers is WHEN IN DOUBT, THROW IT OUT. Foodborne illness (aka food poisoning) is serious business. Beyond flu-like symptoms or the "24-hour bug," foodborne pathogens can cause chronic illnesses and even death. If you are even the least bit suspicious, don't eat it. My personal mantra: BE FOOD SAFE, NOT SORRY.
Be safe everyone, and good luck weathering the storm.