As a follow on to the above, koi are generally kept in a koi specific pool, although people do try to keep them in goldfish ponds and if introduced into a mature pond at around 4" can appear to settle without a problem. Until they start to get bigger and bigger.
A koi specific pool would be a large pool devoid of plants with bottom drains and heavy external filtration, Many people off-set the pool's barren look by creating a japanese garden around it with walkways, japanese specific plants and tubs and sometimes a bridge.
Koi, certainly in the UK, are not that easy to breed. Where goldfish tend to spawn naturally as the water warms up koi quite often need an inducement.
Most serious breeders will keep a spawning pond and as the females become plump with eggs will tranfer one female and two males into the pond which will have had artificial spawning mats introduced for the fish to spawn in.
Spawning is induced by a large water change which will drop the temperature a couple of degrees and usually kick starts the whole process. The fish are watched the whole time by the breeder as the whole process can become very aggressive risking major damage to the female. Once completed the fish are quickly netted and transfered back to the main pool to avoid too much egg eating.
Koi like most fish can be hand spawned, or stripped, and the eggs and milt mixed to ensure maximum fertilisation, but this should only be undertaken by an expert or the fish could be badly injured.