From levels 1-100, fishing will usually take 1 successful skill to level up, but as you progress, you will notice that it will begin to ask more catches for the levels to go - after you hit 125 fishing, you can learn Expert Fishing from Booty Bay by buying the Expert Fishing Manual.
At 225, you will need to visit Dustwallow Marsh to talk with Nat Pagle, where he will ask you to do a quest for him to be able to unlock Artisan Fishing (up to 300)!
Nat Pagle will say you need to catch 4 fish for him, they are:
Feralas Ahi - West from Camp Mojache in Feralas, you will see the Verdantis River, this is the spot you can fish at to eventually catch one.
Sar'theris Striker - South from Shadowprey Village, you will find the Sar'theris strand, in Desolace.
Savage Coast Blue Sailfin - Savage Coast right outside Grom'Gol's Base camp in Stranglethorn Vale.
Misty Reed Mahi Mahi - East from Stonard, where the murlocs are at, in the Swamp of Sorrows.
Once you have obtained all 4 rare fish, return to Nat Pagle to obtain Artisan Fishing Skill!
To obtain Master Fishing (over 300 skill), you will need to buy the Master Fishing - The Art of Angling book from Juno Dufrain in Zangarmarsh, he's right outside the Cenarion Expedition's base in that zone.
To fish in Outland, it is recommended you have over 325 fishing (at least) since the first area you can send your line in is Zangarmarsh. This will make you unable to get fish unless your level is very high. Remember, fishing levels can be obtained anywhere, you could even level your entire fishing 1-375 right within Orgrimmar or Stormwind!
Upon your travels, you may find a journal in one of the wreckages or schools of fish you fish at, within an item called a "Curious Crate". This item will allow you to track schools of fishes down on your minimap should you enable the ability!
The amount of casts required for later levels are a lot, but fishing out motes of water from Nagrand or Zangarmarsh is very rewarding in the end since not many go for it!