How can I prevent ankle sprains?

Proprioception. Google "ankle proprioception exercises" and you will find a wealth of techniques to increase this ability and strengthen the ankles.
Therapy. The best way to prevent ankle sprains is to keep the muscles around your ankle strong.
PREVENT. Specifically applied taping before an athletic activity, an AFO, or ankle brace may help.

Related Questions

How can I prevent another ankle sprain?

Wear proper footwear. That is supportive and well fitting. Orthotics will also help provide support and stability. Have you had a history of sprains? If so why? See a podiatrist.
Ankle sprain. To prevent recurrent ankle sprains you have undergo rehab. Physical therapy will help strengthen the ankle and also work on propiroception. Which helps with balance of the ankle.
Strengthening. You need strengthening exercises through an Athletic Trainer or Physical Therapist.

How can I prevent spraining my ankles in heels?

Wear proper footwear. That is supportive and well fitting. Orthotics will also help provide support and stability. Have you had a history of sprains? If so why? See a podiatrist.
Keep the heels. 2 inches or lower, try to avoid straps and stick with a closed heel.
Lose the heels. At this time, you're better off with flats and/or sneakers and possibly starting physical therapy with an evaluation by your podiatrist. Most likely you have some balance loss and proprioception imbalance associated while in heels. This needs to be evaluated and checked out.

How can I prevent spraining my ankle while playing sports?

Ankle strengthening. Ankle joint strengthening exercises will help. I recommend you google "ankle strengthening exercises" and perform them.
Ankle. To prevents spraining your ankle you should wear an ankle brace when performing sporting activities.