Here is a list I have been given by a Koi farmer, guess it's a good start
Peas
Tomatoes
Cucumber
Duckweed
wheat bread
orange, lemon, grapefruit slices
Romaine lettuce
watermelon
Honey nut or reg. cherrios
Water Hyacinth
worms, georgia reds, earthworms,night crawlers pinks.
All fruit must be seedless or have the seeds removed.
I feed them more as treats, I found that can english peas, and baby lima beans are very well liked by Koi and large comets, Cherrios the bigger koi like them more but broken up the smaller fish enjoy them too, Cucumber and watermelon they will chase and play with but be sure it gets all eaten, Don't let it get into the skimmer, YUCK! as for how often, I feed most natural fruits and veggies once a week or so, cherrios get treated once or twice a day. I'm intrested in seeing what others post as well.