The majority of golfers tend to hit AT the ball instead of swinging THROUGH the ball. Their hands generally stop somewhere near to their crutch, the clubhead subsequently catches up with (or even overtakes) the hands and then the wrists unhinge themselves, throwing the clubhead at the ball.
What you should be doing is hitting
through the ball with the grip leading the way and the hands staying in front of the clubhead right through the shot, or at least until your follow through dictates the necessity for the wrists to unhinge as the club travels around your body into the finish position.
An impact bag is an excellent piece of equipment to help you get this feeling of hitting down into the ball, although you can practice this without one. Here's a picture of the impact position....

As you can see the grip and hands are ahead of the clubhead, and this maintains the LAG that you have generated during your backswing. Here's another....

The idea here is to hit the bag with the SHAFT of the club, that way the clubhead will be behind the hands and will be able to hit the ball with a slightly descending blow (then taking a small divot). It also promotes the weight shift to the left side and the rotation of the hips. All round an excellent piece of equipment.
In both pictures the hands appear to be in front of the left leg at impact! and certainly ahead of where the ball would be placed. Excellent for helping you to bring the clubhead to the ball from an INSIDE swingpath. If you slice the ball then you should try this, most slicers are waaaaay back from this position with the clubhead leading the way instead of the grip.
If you don't have an impact bag then you can still practice this drill, best done in slow motion without a ball until you get used to it, after which you can speed up little by little until you are actually able to take small divots directly after the spot where the ball should be. If you aren't able to take a divot then your weight is probably incorrectly positioned too far to the right of your swing, or your initial setup position is wrong.
Here's the 2 video's relating to the two pictures above...
http://www.youtube.com/watch?v=wSK7M8iCaH0http://www.youtube.com/watch?v=h2VKacwXr_w