THE RIGHT WAY
I have been a Giant tuna buyer for the past 15 years, i work with a fish house in japan. I spent 6 MONTHS learning the proper way to handle fish in japan.
Most of the methods posted on this board will work fine, but allow me to explain a few things.
There are really 2 steps to the proper chilling of fish, lets assume it was properly bleed and butchered.
FIRST STEP IS TO COOL THE FISH DOWN, it is very important the fish is cooled down BEFORE you place in cooler or box for storage or transport. Not cooling the fish first causes your storage ice to melt and the water will soften the flesh if allowed to sit in it. This problem most often occurs when fish are caught then put in a cooler without being cooled down first, the ice in your box will melt trying to chill your fish, INSTEAD of keeping the temperature of your cool.
So the right way is to have a extra cooler or a garbage pail works well too.
You create a brine solution of 2 parts ice 1 part salt water, place this in your cooler or pail, then prepare your fish and place in the brine solution for 1 minute per pound of weight, ie. a 50 pound tuna needs to stay about 1 hour in the solution before you remove it. this is an approximate time , you can leave them in longer.
Now after you remove the fish from the brine solution, you then put it in your fish cooler, pack the carvity with ice and surround your fish with ice as well.
If you want to maintain the color of the fish, wrap it in newspaper or rice paper before you ice it down in the stoage cooler. DO NOT DO NOT USE SALT IN YOUR STORAGE COOLER, THERE IS NO NEED FOR IT AND IT MELTS YOUR ICE FASTER IN THIS APPLICATION.
Ok, I know you are thinking, why this way..... when you pack a fish in ice, there are lots of air poctes between the ice, these airpockets do not allow for proper cooling, in addition due to the shape of the ice it is not in direct contact with the fish every, no contact no cooling. so the slush solution used, allows for direct contact with the fish and no airpockets to reduce cooling effeciency. also the rocking of the boat makes the cooling solution circulate around the fish which greatly helps colling as well. this make a HUGE HUGE difference in the cooling of your fish. I can't tell you how many times i have take a core temperature from a tuna that has been iced down for 12 hours or more only to find the internal temperature in the 50-60's range because the fish was not properly cooled down before being iced for storage.
Do you think that all this extra work is not worth it or it doesnt really make that much of a difference ???
Let me prove it to you easly with this test.
Go get 2 beers or soda in cans, get 2 small container and some ice and salt water. take one container fill it with ice only and bury one of the beer cans in ice.
take the other container make a brine solution of 2 parts ice and 1 part saltwater, then place the other can into this solution, now gently spin (rotate) the can in the solution for ONE MINUTE. now take both cans out of the containers, pop the tops and take a sip, you will instantly understand the difference.
By the way, this is a great way of cooling down any hot drink in VERY VERY FAST time, you can take a warm drink and spin it in the brine solution for 1 minute and it will become ICE COLD.
I hope this helps with some of the confusion of cooling and iceing fish properly.
Bleeding and preparing fish is a whole other matter that would be too lenghty to cover here. Remember i spent 6 months in japan learning to handle and prepare fish properly, and by japanese standards i am still a "amatuer" at handling fish, as most fish technictions spend 3-5 years learning the trade.