Fish can be cooked on a range and a fire.
Small tip for players, if you are bored to catch fishes and you want get them easier way. There is one way to get lots of noted raw fishes, lobsters/swordfishes/sharks. Monster name: Brime Rats
Brim rats drops often nice amount of noted raw fishes, it doesn't take long time to kill one or ten..
You can obtain Cooking Gauntlets, if you meat the requirements of the Family Crest quest. You will reduce the chance of burning food with these gloves.
The following table shows you when that you will stop burning a type of fish on a range or fire.