So, here's a greatly simplified way to find each of the forehand grips. Just center the base knuckle of your index finger over . . .
Continental: the upper right slant.
Eastern: the side plane.
Semi-Western: the lower right slant.
Full Western: the bottom plane.
You probably observe that each grip switch, going from Continental to Western, is essentially a rotation of 45 degrees clockwise.
Can you see why the Eastern grip is the classic forehand grip most commonly taught to beginning students? It places the palm on a plane parallel to that of the strings so that your palm faces the same direction as your racquet. With your wrist straight and relaxed, the Eastern grip results in a vertical racquet face when your racquet is even with your front hip. This is the most natural and physically most secure relationship between body, racquet, and point of contact. It's also the most versatile forehand grip, because you can easily tilt upward for slice or keep the racquet face vertical to hit topspin.
So why would anyone ever use a grip other than Eastern? In a word, topspin.
With the same wrist position and point of contact as an Eastern grip, the Semi-Western and Western grips result in the racquet facing toward the ground, at a 45-degree angle for the Semi-Western and straight down for the full (a.k.a. extreme) Western. When most players first try these grips, especially the full Western, they usually hit the ball into the net. But, once a player learns the corresponding strokes, which are quite different from the classic Eastern, the result is a lot of topspin. These grips are less versatile than the Eastern and are poorly suited to slicing or handling low balls, but many power players find that these grips provide the accentuated topspin they need to bring the ball down into the court. Although some players, like Pete Sampras, can hit plenty of power and topspin with an Eastern grip, the average forehand grip on the pro tours now is Semi-Western.
The Continental grip is rarely used for forehands anymore. In its heyday, it was used for forehands, backhands, serves, volleys, and overheads, the main advantage being no need to make any major grip changes. Its great disadvantage as a forehand grip is its unsuitability to hitting topspin. With a Continental grip, the racquet wants to tilt upward, making it well suited to slicing the ball, but if you swing low-to-high, as you must for topspin, and the racquet tilts up at all, you'll send all but the softest shots well off the court.
Additional resources:
Classic Versus Western Forehand
Evolution of Pro Forehand Grips
