First off, you are doing an achievement not the quest, so don't get those confused. You can track your achievement via the journal->general->Maer Dualdon Fisherman. This tells you how many fish you have caught.
You can only fish if you have the quest to fish. You get the quest from Catti-brie. I had to do one quest for her before I got the fishing quest.
Once you get the quest she will give you a fishing pole. Go to the shore in the zone and look for columns of light in the water. In front of the light should be little sparkles on the ground. Stand on/near the sparkles to get the option to press A to fish.
Be sure that you have several open inventory slots as there are different kinds of fish. You can also fish up a pile of crabs in addition to your fish. If the crabs hit you before you loot the fish then it closes your inventory window and you can't loot the fish.
The quest says to catch 200 fish but I think the quest is referring to 200 weight worth of fish because the number jumps from 10-30 depending on the fish you catch. If you want to get the achievement quickly then only loot the light weight fish to get more fish caught for your quest. Once you hit 200 weight in fish then you can no longer fish until you get the quest again on another day.
*note* You can delete the fish from your inventory if you want to get the achievement right away. Just make sure you delete the fish before you reach 200 weight of fish or the quest will complete and you can't fish anymore. -- credit to Texans2k2