What is the fastest way to heal an sprained ankle?

Rest, Ice, Compression, and Elevation will heal your ankle quicker.

Hydrotherapy methods will also help for a quicker heal.

Fill two buckets....one with cold water and one with hot water.

First....Submerge foot in hot water (NOT scalding) for two minutes duration trying to take the joint through as much range of motion as possible inside the water without hurting yourself. Then transfer your foot from hot water bucket to cold water bucket and submerge foot for two minutes with your foot completely at rest. Repeat this hot therapy/cold therapy process back and forth from hot to cold water every few hours 3-4X a day. Always be sure to end session in cold water.

The hot water and range of motion exercise will increase your blood vessels while the cold water decreases them and puts them at rest. Going back and forth with this process creates a pumping effect in your blood vessels which helps to clear inflammation and fluid from the injured ankle.

As soon as you are able to, begin to place weight on foot slowly while you are seated. Do not do this while standing!

Repeated activation of these nerve fibers in the injured area will help restore strength to the surrounding ligaments and muscles, as well as promote better circulation in that area which leads to much quicker healing.