How can I help speed up recovery time to my sprained ankle?

Rest, PT. Ankle sprains usually take 6-8 weeks to heal. You can speed it up with ice, rest, bracing and physical therapy but they still take time.
R.I.C.E., Therapy... Initially, r.I.C.E. Is indicated to minimize the extent of inflammation and pain. Early passive and active range of motion exercises and a guided physical therapy program may help hasten recovery. Therapy should include achilles stretching, peroneal strengthening, and proprioceptive and agility drills. Medical evaluation is recommended to rule out more serious injury.
Consult your doctor. It is common for one to experience pain for several months following an ankle injury. Ankle braces and aircasts may be of benefit in the initial phase to help immobilize and support the area. Later on, the ankle will need range of motion exercises to improve strengthening. Consult your physician to see if physical therapy is right foot you.
Ice and . Immobilization to begin with and then range of motion and strengthening. Your doc needs to decide when to allow you to begin rehab. I don't know how severe or to what extent your injury is.