The very fastest leveling is barbarian style fly fishing, which requires you to unlock the ability through Barbarian Training. Makes no profit, though. Just below that is Shilo Village fly fishing, which requires you to do the Shilo Village quest. Makes very minimal profit, but you obtain things for slow but cheap cooking training. If you haven't done Barbarian Training or Shilo Village, and have no interest in that, below Shilo is fly fishing in River Lum. Fish a load, drop all, fish another. A bit slower than Shilo, and you don't get to keep any of your catch.
Slower than these, but far the best way, in my opinion, is fishing monkfish. It's about 35K xp per hour, but it makes a lot of profit (about 120k/hour selling raw, 95k/hour selling cooked), and gives the option in the end for getting 99 cooking for free (but will lessen the profit). Only place to fish monkfish is in the Piscatoris Fishing Colony, which is secluded from everything (fastest way is with fairy ring) and requires the Swan Song quest.
Good luck
|