Sorry 'bout the knee. Had several sprains at the ankles...they all can suck. Having said that, the best way to strengthen your ligs is first to let them heal. Don't rush the process, you will only weaken them. A sprain can take quite a bit longer to heal than a fracture[I'm generalizing here, of course degree of sprain is a big factor].
Pro athletes are always returning "ahead of schedule" only to return to the injured list soon afterward. The knee is an important joint that will only improve AFTER it heals to begin with.
You may wish to use a brace to help support the knee for a while.
How did you hurt it?
Hope I helped.