Archery is a Combat Skill that requires an equipped bow and carried arrows of various kinds.
Arrows can be found directly outside of the Tutorial Cave, a stack of 1000, in the middle of a ring of fungi. Note that there is a slow reset timer on these items.
A bow might be found in the cave, or bought in the town in the zone outside the Tutorial Cave. It equips to the 'off hand'. (Can they only be offhand?)
Arrows can be changed to deal, for instance, Poison Damage. (how?)
The Archer Trainer is in the village (Serlune? Verify) in a building not too far from the pond. He teaches Archery to level 1 (you get the first skill) and Fletching as well.