Also see: Fishing for info about the mechanics, Fishing Poles for the different kinds of rods used to catch them, Weight for all the different weight values of each fish, and Wall Trophies for all the different fish trophies and how to obtain them.
Throughout fishing, Fish are used in collecting Glim/materials. After obtaining a suitable pole, players can fish in different liquid types to find different varieties of fish. Most common and uncommon fish can be caught anywhere within the proper liquid; however, rare fish require specific conditions to be caught, in most cases specific biomes. Some of them can only be caught in pools.
When looking for rares, the position of the lure is what determines which ones will be available, not the position of the character. Any suitable liquid within the proper conditions will qualify, including those contained in cornerstones (currently only possible for water and chocolate). You can use /debugtext in order to see the height you are on, (xxx, height, zzz).
Sea of Regret doesn't count as regular water and cannot be used as a fishing spot.
Note that after Reeling in the Stars update, fishes can no longer be fished in club worlds. Also, the glim collected has changed. Now, when loot collecting fishes, they will give a variable amount of glim, based on the rarity and trophy level:
Some fishes require you to fish in some liquids that do not spawn in the required biome (like water on Dragonfire Peaks). In the case of water and chocolate, this can be easily solved by placing Face of Flow or Cocoa Cascade, or shooting with Palashien, Soul of the Sea (generates water where it lands), in the respective biome. On the other hand, with lava and plasma this could get annoying, as you cannot generate them. In order to fish in those liquids, you could find a Dragonfire Peaks Biome for lava or Neon City/Luminopolis Biome for plasma next to the biome you want to fish on. Using bombs or your laser, you can move those liquids to that biome. Another option is to find a dungeon containing those liquids. When fishing in Geode Topside this in the only way to do it. There are some 5-star dungeons containing them.
Fishing (128)
Water (30) These fish can be caught using any fishing pole on Water blocks.
Enchanted (5) These fish can be caught only with the Lady of the Lake or Royal Reeler fishing pole equipped. Don't forget that enchanted fishes can only be caught in water blocks.
Pools can be randomly found whilst adventuring different liquid types. Pools are pre-set with a variable amount of different fish, which means, fishes from pool 1 are not obtainable in a pool 3 pond. This information will be especially helpful for when you eventually get to fishing Deep Ones. Example: Pink Cubal (Water pool 3) cannot be fished when you’ve already fished up Froggy (Water pool 1) from said pond. You’ll have to move to a new one. Note that on Tuesday, the bonus fish chance may grant you fish from random pools of any liquid type.
If you are playing on PC, there is a mod that sets a display on pools, making them easier to find and also shows how many fishes are left inside the pool. You can download it on Steam or Trovesaurus. The first image is how pools look like in game without the mod. Last two are pools with the mod installed.