There have been many different opinions on this topic, but very few instructors tell you WHY you should grip the club a certain way. The reason that the grip is SO important is because it is the only part of your body that controls the clubface, your hands.
If you have a tendency to slice the golf ball, try this:
Move both hands to the right so you can see one or two knuckles (top knuckles) of the left hand. The most important part of placing your grip is to make sure both palms are facing each other. So adjust the left hand, and then adjust the right hand so that your right palm is facing the left palm. - Strong Grip
If you have a tendency to hook the golf ball, move both hands towards the left (palms facing), and you should see no knuckles on your left hand. - Weak Grip.
When I mention the knuckles that I have been referring to, here's what I mean.
1. After you have addressed the golf ball and you look down at your hands from the address position.
2. You should look at your left hand to see if you can see any knuckles.
Now let's talk about grip pressure.
Tip: The tighter you grip the golf club; the more the golf ball has a tendency to go off to the right. The looser you grip the golf club; the tendency will be for the golf ball to go off to the left.
Most of the time when I am giving a golf lesson, I can see the whites of my student's knuckles because they are gripping the golf club so tight. This is incorrect! Hall of Fame golfer Sam Snead once said "Hold the club as if you are holding a bird in your hands." Another quote that I once heard is that you should grip the club like you were holding a tube of toothpaste.