What typically causes ankle sprains?

Inversion. Typically, inversion of the ankle causes the most common ankle injury: a sprain of the anterior talofibular ligament.
Inversion. When your ankle turns in , it stretches the tissues on the outside of the ankle, resulting in a sprain. 90-95% of all ankle sprains happen when the foot/ankle turns in. Weak ankle muscles are often the culprit.
Rolling it over. An ankle sprain is generally done by rolling the foot over the outside edge, putting too much pressure on the tendon running along the outside of the ankle and partially tearing it. A sprain is basically a partially torn muscle/ tendon combination, with swelling and further stretching causing more damage. There are other ankle sprains injuring other tendons, but this is the most common form.