Crafting skills (Alchemy, Enchanting and Smithing), of course, increase mostly by crafting items. Some skills, specifically Lockpicking, can increase when an attempt to pick a lock is unsuccessful (when a lockpick breaks).
However, most skills must be used in combat in order to gain the increase.
Conjuration increases a little bit each time the Dragonborn summons a Bound Weapon or creature, for example an Atronach. The level of a given skill is increased as the skill is used successfully - Archery is increased when an arrow hits its target Destruction is increased when a spell causes damage to the target Sneak increases when the Dragonborn remains undetected in Sneak mode while in range of NPCs who otherwise could detect them, etc.
