This stroke is called pushing. It generates underspin and is used to control the length and placement when returning an underspin ping pong ball. It is mostly a defensive shot but it can be used to throw the opponent off balance and set up an attack. The forehand push is almost exclusively used as a technique for receiving a short underspin serve.
A short, quick, stroke imparts underspin and the ball is placed carefully to avoid an attack. After the stroke, recover immediately and prepare to attack. Step in towards the ball with your right foot and shift your weight to the right. Raise your forearm a little with the racket open. Move your forearm forward and brush under the ball. Contact the ball here. Follow through to carefully direct the ball and then recover. Move towards the ball; balance your body before you touch it. Push forward under the ball and recover.
Unlike the backhand push, spin is not as critical for the forehand push as the height and length. Since the ball is so clearly in front of you, you can carefully choose the placement. The earlier you take the ball, the quicker the opponent has to react. Recovering from the shot is just as important as getting to it. It is one of the opponent's goals to pull you out of position with a short ball and then beat you with a long attack. A quick recovery avoids that.