You'll need the fishing skill, a hook, bait or lure, string, fishing pole, and a hook.
Bone hook is the easiest one to make.
Bait vs lures: Bait catches fish at a
much faster rate but it is one-time use only.
Bait is preferred in my opinion. Leeches and intestines aren't too hard to come by.
For a more complete list you can search for "bait" or "lure" on
the wiki.
String is
not the name of the item. Items that can be used as string include...
Spindly Taproot - a plant you can pick if you have the Foraging skill
Stinging Nettle - another plant you can forage
Hide Strap - a string made out of the dried hide of any animal (leatherworking)
Plant Fibres - a byproduct of harvesting flax or hemp (farming)
Yarn - created from wool in a spinning wheel (clothmaking)
Silk Thread - an expensive string made from silkmoths (sericulture and clothmaking)
You're more likely to find the ones near the top of that list.
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Left click the string to pick it up and right click the fishing pole to attach it. Do the same with the bone hook and the bait or lure you've chosen.
Equip the fishing pole.
Find a spot with jumping fish like this:

Adventure -> Fish
