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What is the best way to treat a sprained ankle? Is it better to use ice, wrap it up, stay off it?

How about all of the above? The rule of thumb when treating a sprained ankle (or wrist or knee, for that matter) is to follow R-I-C-E.
R = Rest the ankle
I = Ice the ankle
C = Compress the ankle (using a bandage, tape or even a brace)
E = Elevate the ankle

For most sprains, that's all that is needed, in addition to some rehabilitation exercises to strengthen up the ankles again.

Reference: 

Cyrus E. Taghavi and Nelson F. Soo-Hoo. Lateral Ankle Instability. In Current Orthopaedic Practice. April 2009. Vol. 20. No. 2. Pp. 117-122.

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