Ice is probably the first and most important ingredient for quickly dealing with sprains. To treat wrist sprain, get an ice pack or bag of frozen vegetables and place it on the effected area. Ice it for the time till you're comfortable!
You should try to rest as often as possible for the first 24-48 hours. This will allow your injury to rest and heal at a more rapid rate. For sportsmen and other workaholic people, rest might feel boring, so it's better to plan some activities that do not require movement of hands, i.e. watching movies, reading books etc.
Use a tensor bandage to wrap the wrist firmly and securely. Although the bandage should be tight, it should never cause discomfort.
Wrap from the top of the pinky finger up to about half the forearm. It is important to wrap the thumb separately for comfort and wrist placement.
Whether sleeping or lying on a couch, place pillows or folded blankets under the sprained wrist. It is important to keep the wrist above the heart at all times possible. Elevation will reduce swelling and pain, with the added benefit of expediting the healing process.