In the Weapon category you can find the following weapon types that are present in the Elder Scrolls Online: Bow, Destruction Staff, Dual Wield, One Hand and Shield, Restoration Staff and Two Handed.

To unlock these skill-lines on your character you have to find the weapon type and kill a monster with that weapon, afterwards the skill-line will be fully visible in your character skills section. The weapon skill-lines are leveled up by simply getting experience points from any activity such as killing monsters or completing quests.

To level up skills from the weapon type of your choice, you have to place them on your front bar.