Do you wish to filter the koi out of the water?
Do you want to aerate the water at the same time?
do you want physical, chemical, radiation, or biological filtering...or a combination?
basically, pump water thru a screen. That should get you started. Koi will grow proportionally to the size of their home. If you keep them in a small area, expect small koi. If you grow them in a huge pond, they will...you get the idea. Plan your filter around the size of the water you are going to filter. I forget the rule of thumb for the ratio of water circulated vs total water..