When a knee (or any other joint) becomes injured, there is often a period of swelling and inflammation over several days that can hamper normal actions. By starting the RICE treatment method, the inflammation and pain can be minimized, thereby decreasing the amount of time that an athlete or "weekend warrior" is out of the game - or out or work.
The "R" stands for REST. Some injuries just cannot be "played on" or "worked out" with activities. When a knee is swollen and painful, the best advice is to take it easy and listen to the symptoms. For some injuries, the resting may be only for a day, but for others, it may be a few weeks.
The "I" stands for ICE. Inflammation in a swollen knee leads to a puffy, tender joint. The fluid that builds up in the knee is uncomfortable, so an ice bag on the knee can slow down the process of inflammation and hasten your recovery. Ice should never be placed directly on the skin, as cold injuries like frost bite can occur. Using a towel or pillow case on the knee with a sealed ice bag on top for 20-30 minutes can help a lot. Alternating 20 minutes on, then 20 minutes off, works well. The swelling will slow down, and the knee will hopefully start to feel better.
The "C" stands for COMPRESSION. An elastic wrap or bandage that is applied around the knee can limit the build up of inflammatory fluid. The sensation of "snugness" also tends to give the injured person more trust in the knee when walking. No wraps or bandages should be placed tightly on a knee, though. If the knee is "strangled" with the wrap, then blood cannot get to the knee or feet, which can have serious consequences. It should never be painful to have a wrap or bandage on the knee.
Finally, the "E" stands for ELEVATION. By elevating the leg to the level of the heart or above (on pillows or a chair while sitting/lying down), the accumulated fluid can exit the leg and head back to the body easily. This makes sense and it is a time-tested treatment for swelling. Also, the throbbing that normally accompanies a recently injured extremity will lessen when it is up in the air.
Basically, you can't go wrong with starting to treat any mildly injured extremity with these guidelines. Always consult your physician if pain is severe, if the swelling continues to worsen, or if numbness and tingling accompany the sprain.