This is just the same as free players: Head to Draynor Village with a fishing net. Go south of the bank until you see some fishing spots. You will be here for a while. It is not exactly lighting training, but it will have to do. By level 20, the level gains will seem slow, and it is time to prepare for the next step.
Get feathers either by buying them or by killing chickens for them. If you are level 15-40 combat, I recommend killing them because at your level, you will save money for bigger, more important purchases, and you will kill them relatively fast. When you have a lot of feathers (I recommend at least 5000), go to Port Sarim (just west of Draynor Village and south of Falador) and buy a fly fishing rod for about 5gp.
That is right, you are going to get about 2 million experience at the same spot. However, it will go by fast. Even at level 60+ fishing, you will be gaining two or three levels a day easily.
Grab your fly-fishing rod and about 35,000 feathers. If you cannot afford them, just get about 5k feathers off chickens and head to Shilo Village (must have completed the Shilo Village quest). In Shilo Village, with your fishing rod and feathers, just north of the bank should be a few fishing spots. Fish an inventory of them, and sell them to the fishing store just south-east of the river. Now buy back as many feathers as you can afford and fish another inventory. You should never run out of feathers like this.
Stay here fishing and banking/selling until you have used up all your feathers and/or hit level 80. It will take a lot less time than you might think.
Another great place to fly fish is directly west of the Fishing Guild. The spot is a fantastic place to fish, which it is just north-west of the Moss Giants. So you ask... where's the bank? You can't bank here and efficiently fish as well as Shilo Village or Barbarian Fishing but this is faster than Shilo Village if you sell the fish. Rasolo is directly north of the fishing spot and near the house. He accepts the fish through player stock and fishers can camp out here until they have no feathers left.