Someone told me that one can kill a fish by putting it in iced water. He stated that it'll kill the animal extremely fast and without any pain.
I have my doubts... Can anyone explain why this should work? Or is it nonsense?
You can kill tropical fish by freezing them, or even just letting them cool down. From the outdoors perspective, most game and edible fish are not tropical. There is a post on a sister site Fish “coming back to life” after being frozen and there are many Google finds about frozen fish coming back to life. From personal experience I recall my grandfather putting a fresh salmon in the freezer and when days later we put it in the sink to defrost, it started flopping around still alive.
In short, putting most fish in cold water or freezing them is not going to reliably kill them. Some die, some don't. Whether it is humane remains questionable: I'm not sure there is enough evidence to support a conclusion on the fish's experience of being frozen. Many game fish (and pond goldfish) are frozen during winter as part of the natural life cycle.
Ice water will not kill any fish quickly. Some fish even live in ice or icy water. A tropical fish may go into shock, but it won't die right for a long time. I think people may believe the fish is dead because the body has stiffened, but that's just a function of the cold and doesn't indicate a dead fish.
The fastest way to kill a fish would really be to behead it, but that assumes you are cleaning it immediately, and it can also make filleting a little more difficult. An alternative is to pour distilled grain alcohol over the fish's gills. That will also kill it quickly as well. The best way in my opinion is to cut the gills out at the bottom of the gill covers. This bleeds the fish out, helping it to die and also has the benefit of improving the fish for eating.
Because they are cold-blooded, fish will live a long time, even if they can't be resuscitated. So all you can do is the best you can. Place a folded wet towel over the fish's head so it's in the darkness and it will calm down significantly. Anecdotally, it may help the fish as much as it helps you.
It is absolutely not humane - in fact it is by FAR one of the most CRUEL methods to euthanize a fish. Regardless of them being tropical or not, before they are sufficiently cold enough to die, their blood crystallizes and they basically end up with ice shards shooting through them. Ouch. This is a very common question on aquarium forums and message boards though.
A better method to euthanize a pet fish is to overdose it with clove oil in a bowl of its tank water (clove oil is ordinarily an anesthetic is smaller quantities).
A better way to kill a fish you want to consume (or pet fish if you have the knife and fortitude to do it) is to simply chop its head off in one blow. Or to sever the spinal column (I think that would do it).