The fishing instructor is one of the many NPC you will probably meet on your journey. He is located on the tutorial island as well as Dorpat's Dock.
"I'm here to teach you about Fishing."
"First you need to equip a Fishing rod by clicking on it inside inventory."
"After you have equipped the Fishing rod you have to stand on the beach line and click on the water."
"You can only fish in places where a yellow text - Fish is visible. To fish with a fishing rod, find a tile named Fish - Fishing Rod."
"Talk to Cooking Instructor to find out how to cook the fish."
Disclaimer: This is word for word from the game, anything that sounds weird or is grammatically incorrect is purely the game.