For many players, moving the ball from right-to-left isn't the issue; making sure the draw doesn't turn into a hook is. All golfers slip into bad habits. When you miss fairways and greens, you probably miss them left. Chances are you're hanging back on your right side through impact while your hands turn the club over, resulting in too much hookspin. Here's how to make sure you transfer your weight fully to your left side and take the hook out of your bag.
Fire the Right Side

Believe it or not, a hooking problem can
often be the result of the right side being too passive.
Instead of the right hip and shoulder driving through
the ball, they hang back on the right side. The hands
are left to lead the clubhead into impact, and they
inevitably release the club too early and hook the ball,
because your center of gravity is too far behind the
ball.
To counter this, make your normal backswing, then concentrate on rotating your right hip and shoulder past the ball as you swing down and through. Keep them level with your left shoulder and hip as they rotate. You won't be able to move them past the ball, but that's the feeling you want.
This "firing" of the right side keeps your center of gravity over the ball, making it nearly impossible to release the club early and hook the ball. Your shot pattern will be straight, left-to-right, or slightly right-to-left, depending on your angle of attack. But the big hook will no longer be a part of your game.
Drill: Isolate the Right Side

To get the feeling for activating the right
side, isolate it by hitting 5-irons with your right hand
only. Tee the ball up as you would for a drive, take
your normal stance, except leave your left hand off the
club. Swing to the top, then swing through. Only by
firing your right side and transferring your weight
fully to the left will you be able to make solid
contact.