What is the best course of treatment for a sprained ankle?

Several things: One should elevate the extremity, use an ice pack, use an elastic bandage (not too tight) and take some Ibuprofen (if not allergic). I am assuming you don't believe or have been told it is not broken. Rice--rest, ice, compression, elevation. If there is concern for ligamentous instability, fracture or other issues, then you should see your pcp, orthopedist or sports medicine doc.

RICE: Rest it, ice it (bag of frozen veggies works in a pinch), compress it in an ace wrap or brace, elevate it as much as possible and take Ibuprofen or alleve to decrease the pain and swelling. If you cannot put any weight on it at all you should see your doctor. You may need crutches or further evaluation.

Rest: Ice, elevation, NSAID for pain. I suggest you have an x-ray if pain persists.