The primary objective (both short and long term) for the aquarist is to supply oxygen to the tank and move water (even periodically) about in the tank. This is bare bones survival and some of your tank's filtration systems (wet/dry trickle, canister filter) will not be functioning. The nitrifying bacteria which resides in the tank (on the live rock, tanks walls, etc.) will live and continue to process ammonia, nitrites and nitrates if O2 is supplied at least periodically.
Here is one method which is easy to do and actually works:
Take any type of clean cup, pitcher or other container, scoop out and fill it with aquarium water.
Hold the filled container some distance above the aquarium, and pour the water back into the tank. Repeat this process numerous times.
A larger volume of oxygen is generated the higher the water is dispensed from above the aquarium, and the number of repeated times this is done.