A mild ankle sprain takes around 6 weeks fully heal.
Most mild ankle sprains heal with some ice and rest within 6 weeks and rarely need medical treatment or an emergency room visit.
For a more severe sprained ankle it may require an emergency room or doctors visit and medical treatment.
If the ankle sprain is more severe then it can take 2 to 3 months for the sprained ankle to heal.
When I've had a mild ankle sprain it healed with use of some ice and rest within 6 weeks.
You should rest as often as possible and not walk too much on the sprained ankle and take it easy until at least 4 weeks.
Then gradually return to any normal activities that you normally do.