What are physical therapy exercises for a finger?

Movement: It depends a lot what exactly was the injury to the finger. In general if the skin is intact, and there is no infection or stiches present. Washing dishes in warm water is a really good home therapy. The warm water helps to loose the joints, soften the skin, and provides a gentle task that you can easily control by using your hands.

Different ones: There are different exercises depending on what finger and what joint was involved. Using a tennis ball to squeeze is a good basic exercise.