Use a Driver
The first tip for putting from the rough is to simply use a driver instead of your traditional putter. The larger club head of a driver will allow you to fight through the thick, high grass easier and be able to putt the ball with both more power and accuracy. Once you become comfortable with taking such short shots with such a large club, you will find it successful most of the time.
Chip Shot Approach
Another tip for putting from the rough is to approach and play the situation as if it were a chip shot but using your putter. Lower your left shoulder (right shoulder if you are left-handed), place the majority of your weight on your left foot (right foot if you are left-handed), then stoke down and follow through well so you can receive a minimal amount of ball loft but with enough power so the ball can get close to the cup.
Cross-Handed Putting Grip
The best method ofr putting from the rough is to use the cross-handed putting grip. Place your right hand (left hand if you are left-handed) at the top of the grip, with your thumb resting over the top with your left hand (right hand if you are left-handed) right underneath it with your right thumb inside your left palm (both hands should be together). This putting grip method will keep your wrists straight and will allow you to slice through the rough and gently lift the ball out of it. Using the cross-handed putting grip with a chip shot approach should help you be comfortable putting from the rough.