The good news is that tendons and ligaments are designed to stretch and contract- so a simple sprain, where the ligament is simply stretched too far, can return to normal shape and function in a matter of days. More complex sprains, where tissues are torn, can take significantly longer, or may even require surgical repair.
No matter what grade of sprain or strain, initial treatment revolves around R.I.C.E. therapy, designed to reduce the swelling and inflammation around the area, so that it can feel better faster, and heal faster.
R- Rest. Rest the injured part during the initial 2-3 days. Thereafter, gentle stretching is often recommended for simple sprains or strains
I- Ice. Ice directly reduces swelling at the site
C- Compression. An Ace type bandage not only provides support, but also drives swelling away.
E- Elevation. Again, the focus here is to reduce swelling.
Additionally, Ibuprofen is often recommended for a few days, as this anti-inflammatory drug not only helps pain, but acts internally to reduce inflammation.
management of sprains and strains and application of bandages are covered in AHA's First Aid course.