Very surprising that life is still thriving without filtration or aeration for a year!? Hard to believe. Considering all koi do is eat and poop.
Well first things first, test the parameters to see where your starting point is.
I'd say shop around for deals but it sounds like you need equipment now!
I won't say any brand names, since there is a ton out there, so I'll tell you the basics of any pond.
(I've been selling koi for 5 years now)
Get a pump, put it on the furthest and lowest point away from the waterfall.
Pump leads into the biofilter
Biofilter leads to UV Sterilizer (Get a sterilizer, not clarifier)
UV leads to particle filter (Collects all the little specs of leaves and dirt)
Filter to the waterfall
Make sure the waterfall creates a lot of aeration (Position to get as many bubbles as you can, the more spread out and deeper they go, the better)
If the waterfall is insufficient for this, you may need another smaller pump just for a fountain spout..
You can put the biofilter and particle filter together after the sterilizer if that is easier for you, it won't do much difference. I can explain why I put my biofilter before if you want..
I strongly suggest you find out what the pond size is in gallons so you don't fall short on equipment, or pay too much.
Can't go wrong with too much, only your wallet will feel the pain.
Too little could be disastrous..
Since the pond has been left alone for such time, the fish have become pretty accustomed to the water conditions..
I wouldn't hook up all the filters at once because of this.
Most important is just to get the pump hooked up first.
I would place the filter media into the water for a week or 2 (in a sunny spot, but not into the moving water of the pump) just to get some beneficial bacteria growing on there.
Any is better than none.
Try and avoid a nasty nitrogen cycle as much as you can.
