"The basic factor in all good golf is the grip. Get it right, and all other progress follows." - Tommy Armour
Another important grip fundamental to keep in mind is that the palms of each hand must be facing each other. If they aren't, the hands will work against each other as the club is swung, twisting the face of the club and making solid contact with the ball virtually impossible. This unbalanced hand position keeps the wrists from making the correct setting motion on the way back and through the ball.
One good way to test the balance of your hands is to take a book and place it between your hands in mirror position, with your fingers spread slightly apart on each side. Hold the book toward the ground as if it were a golf club and then swing your arms around as if swinging a club. Your thumbs should be pointing upward at waist level. Now complete your swing to the top and then make a swing through an imaginary ball, watching your hands rotate on the downswing, squaring the book at impact, and then again bringing your thumbs to point upward in front of you and on through to the finish.
Try this drill several times at home to get the feel of how the clubface rotation should work during a swing and how the hands work together to make this happen.