If you are faced with playing a golf shot from greenside rough, the first thing that you need to do is look at the actual lie that you are facing.
If the ball is resting on top of the grass then do not ground the club head, hover it next to the ball. If the club head is rested on the ground, it may disturb the grass that the ball is resting on and the ball may be moved as the grass is moved, resulting in a penalty shot!
Hover the club head next to the ball. You want to hold lower down on the handle than usual to shorten the club length and pull the club head up from the ground. As you play the shot from this lie, you do not want the club head sliding under the ball. You need it striking the side of the ball so holding lower down on the handle will encourage this. Keep your weight even and play the ball from the middle of your stance. Make a sweeping action as you swing the club so that the club head swings towards the ball on a low angle of attack and clips the ball crisply off the top of the grass.
If the golf ball is nestled down in the grass, you need a different approach. With the golf ball low in the grass, you need a steep angle for the club head to attack towards the ball with so that it strikes down to the bottom of the ball in the grass. To achieve height on the shot to get the ball out of the grass, open the club face so rotate the handle of the club to the right to allow more loft or club face angle.
However, this results in the club face aiming right so adjust your feet and stance to the left so that the club face aims back at the target. You need to pick the club head up in a steep action so that you can drop the club head back down steeply and into the back of the golf ball. To encourage this steeper swing action, place more weight on to your left side and play the ball more forward in your stance. Take a few practice swings through the grass to get a feel for the resistance of the grass and the force that you will next to use when playing the shot and then play the shot and hold your follow through off. This means keep the club head lower than your hands as you follow through to encourage the club head to strike down to the bottom of the ball.