A very simplified way to explain the game of tennis to someone is: Brush - Pull - Snap.
 
Most ground strokes should be Brushed. Brushing up on the stroke actually forces the ball to come down. Many players try to guide or push their racquet through the ball. The great players, like an artist, use the racquet as a brush. Brush up on the back face of the ball. Why? This creates topspin, your best friend on the ground strokes.
 
Most volleys and under spin shots, including slices and chips, should be Pulled. Pulling down on a volley or chip actually forces the ball to lift up. As a right hander, hitting a forehand chip or volley, you might think right to left, high to low or outside to inside. As a result of this you will create friction from the strings to the surface of the ball. This creates control! Do not Push your chips or volleys. Pull them while stepping through the shot.
 
Lastly, on your serves, overheads and bounce-smashes, you should try to Snap your wrist at the ball. Snapping your wrist will actually help force the ball down. Do not Brush or Pull these shots. As your arm goes up to full extension, slow down the arm speed and force the wrist to accelerate or Snap! You will get much more racquet speed and not put so much pressure on your arm and rotator cuff.
 
Try: Brush - Pull - Snap the next time you play.
 
Good luck on the courts!