To start fishing, you must have the correct equipment in your inventory for the type of fish you want to catch. You must then click on the pier and select the "Catch" option. You will then attempt to catch a fish and you will stop once your inventory is full.
Shark fishing used to be slightly different. You needed Level 70 Fishing and a boat in order to go shark hunting, and unlike the other fishing methods, you did not receive fishing experience for catching a shark as you were required to fight it before you could catch it.