A Koi pond is more than a hole in the ground with a liner and some water.
In order to have a healthy, dynamic pond environment you also need a biological filter, a source of aeration, a circulation pump and adequate space, or volume.
It is important to note that all of these elements must work in harmony with one another.
The filtration system purifies the water of wastes, bacteria and other toxins. An aerator supplies air to the water so the fish will have oxygen and the water does not stagnate.
Where is the best place in any pond system to add air or oxygen?
Directly into the biofilter system as close a possible to where the bacteria are sitting. This is why vortex filters and Japanese Filter Matting work so fantastically well together in any serious water ponds system .... but only by pumping plentiful volumes of air around the Japanese Filter Matting matrix.
How much air should you add to you Koi Pond?
Add as much air to your pond as you can using air pumps and air stones to distribute the air (highly recommended for ponds that are heavily stocked). You can add the air directly to the pond, the filter, the waterfall and anywhere else you can think of.
The last note for safety
NEVER - NEVER install an air pump BELOW water level! (Unless you install a check valve in the line!) If at any time your power supply to your air pump is interrupted, water will back siphon down the delivery tube and flood the pump workings, rendering the pump inoperative, to say nothing of the danger of water and electricity coming in contact.