Many pros have many different ways to explain the groundstrokes. Here is my favorite way.
 
On the forehand ground stroke, start with the semi-western grip, (palm more down as if you are bouncing a basketball). First, "set" the racquet out. (Out meaning in front of you) Remember, when you run, keep your hands in front of you, not dangling behind you. Let the racquet take you to the ball.
 
Second, "lay" the racquet back. Let your hips and shoulders take the racquet back. Avoid swinging it back where your racquet never stops in the same place. Do not lay the racquet back until you get near the ball. The racquet backswing should stop when your shoulder stops.
 
Third, "press" the racquet down to the earth like you are palming a basketball down. The more you press down the tighter the arc of the shot will be (more top spin). This allows you to hit with tremendous racquet head speed and with control.
 
Lastly, "brush" the racquet head up the back face of the ball. This "brushing," low to high, south to north, also gives you more racquet head speed plus tremendous control.
 
The backhand groundstroke is very similar, except you must change your grip (bottom hand to a continental grip).
 
In conclusion, on your groundstrokes, "set" your racquet out, "lay" it back, "press" it down and "brush" it up. For simplicity, just say to yourself, "Set, Lay, Press and Brush."
 
Good luck on the courts!