Koi will eat both animal and vegetable matter which makes them omnivorous. They do not have stomachs so they can't eat a large amount of food at one time.
This is the reason your fish spend a great deal of time foraging around for food. Fish will actually eat just about anything that is small enough for them to swallow whole.
The hand-feeding process can be pleasurable for both you and your Koi or goldfish. Instead of throwing the fish food into the pond, take the time to place the food into the water at the same area daily.
In so doing, the Koi will become accustomed to the routine and will, over time, become friendly and trusting enough to be hand-fed. Koi have even been known to recognize there owners' footsteps and follow them around the waters edge.
Taming and training your Koi is a gradual process, but it can be very rewarding. Spending this time with your Koi will also allow you to observe any problems early on.