Taping a sprained ankle yourself is an easy and convenient way to save time (and money) when it comes to ankle injuries and stabilizing the ankle to prevent a future injury - but you have to be sure you are doing it properly so as to avoid further injury. The directions for taping a sprained ankle below are from the American Orthopaedic Foot and Ankle Society.
You first want to be sure you have all the appropriate materials. Typically, you will need athletic tape, padded gauze if you are prone to blistering, pre-wrap, and some sort of adhesive (an easy option would be to get some quick drying spray on adhesive). Make sure the ankle is set in a fixed 90 degree position, with the toes pointed straight to the ceiling. First position the gauze pads on the front and back of the ankle (to help with blisters). Then begin covering the ankle and foot with pre-wrap, starting at the arch and continue wrapping up through the lower calf muscle. Secure the pre wrap in place with adhesive spray.
Then anchor the pre wrap with athletic tape by wrapping athletic tape first around the foot at the arch (one time) and then at the top of the pre wrap, near the base of the calf (also wrapped one time). Then, starting at the top near the base of the calf on the inside of the ankle, position the athletic tape vertically and wrap it straight down the inside if the leg/ankle, around the heel, and up the outer side of the ankle and lower calf (as if it were a stirrup around the foot). You can secure it with at least three strips of tape.
Continue with the athletic tape, wrapping up all the remaining areas of the pre-wrap, so that basically the entire ankle, lower calf, and upper foot are now covered with athletic tape. The final motion of wrapping the foot with athletic tape should be in a figure 8 motion around the foot up and across the shin and around and down the back of the ankle to the arch. As before, this motion can be taped several times. The final product should have the ankle feeling very secure and stable.