Terraria – Cannot turn in quest fish to terraria angler

Hardmode is not required. His appearance is random, and (as of 5/12/2014) there is a bug where if the beach part of the ocean biome is too small, he can appear out on the water's surface instead.

No additional prerequisites have been found. You do not even need an open house slot before he'll appear; mine appeared when all my housing was full.

From the terraria wiki :

The Angler is an NPC that doesn't sell anything, but rather assigns quests to players. Quest objectives generally involve fishing him up rare fish from different biomes, for which he dispenses various rewards.

Also from the wiki :

Once the Angler is acquired, a new Quest is always in effect each day. If you don't complete a Quest before the day is over (4:30am the following day), a new Quest begins, whether or not you speak to the Angler again. It is possible to complete Quests without actually speaking to the Angler to find out what the quest is. Though most Quests require fishing in a specific environment, so your chances of success are better if you speak to him to find out where to fish. Once you complete a quest, you must wait until the following in-game day to embark on another. The Angler may spawn directly on an Antlion, so if the player is not fast enough he will die. If the Angler dies while asleep, he will vanish in a puff of smoke and respawn immediately somewhere in the Ocean biome.

Source

I think this pretty much answers your question. Acording to the wiki you can talk to the angler npc to ask him where to best fish for the specific fish he asked you to get.