Any ham-fisted gorilla can grab a club and start whacking away at the ball. However, if your goal is to improve your swing, the first step is to pay attention to the way you hold your club.
Stand up, let your arms hang loosely at your sides and look at your hands. Notice how they are angled naturally -- you can easily see the knuckle on your index finger and part of the knuckle on your middle finger. By duplicating this "neutral hand position" when you grip your club, you'll more consistently and naturally square the clubface when you swing, increasing your chances of impacting the ball where you should, at the center of the club head.
Gently bring your top or lead hand (left for right-handers, right for left-handers) to the club and hold it lightly in place with your thumb pointing down. You should still be able to easily see the knuckles of your index and middle fingers. The "V" between your thumb and index finger should be pointing toward your rear shoulder -- not your chin. Now, place your bottom or trailing hand below your top hand, taking care to maintain its neutral position.