Archery
Training
From 0 - 30 skill you should buy from the Warrior Guildmaster. After that you need to hold a bow in hand and hit opponents. For more details on training Archery or other melee skills visit the Melee Training Guide.
Weapons
There are two main types of weapons available to practitioners of Archery, bows and crossbows. The former require a good supply of Arrows on hand, while the more technical crossbows fire smaller Bolts at enemies. All of these can be crafted by Bowyers.
Bows are typically slightly faster to fire then crossbows and also usually offer a larger attacking radius. On the other hand, crossbows often pack more punch per bolt and so might be the better choice for a lengthy battle.
The Elven Composite Longbow is the only Archery class weapon that can be used with Poisoning (via Serpent Arrow).
While not technically a weapon, it's worth mentioning that any archer worth his or her salt will be carrying a Quiver with them.
All Archery weapons are Two-Handed Weapons, unless they have the Balanced property. For this reason, when crafting with Runic Tools, you might consider the Lightweight Shortbow.