The legs in the golf swing are primarily the platform for balancing the trunk and swinging the arms. Without the stability of the right leg and the right foot, the power which comes from the motion of the arms, the turning of the hips and trunk, and the ability of the wrists to act as a hinge and release the clubhead through the ball, is diminished. A drill that will help demonstrate and allow you to feel this is just get down on your knees and swing the club. You will feel the power that comes from the hips and trunk while doing this, eliminating your legs from the equation.
The legs and feet are the foundation that allows you to generate the power. While the legs and feet provide the platform, the arms and trunk have to work in harmony with one another. The arm swing and the rotation of the hips and trunk help the player to transfer the weight to the right leg and foot. As the trunk starts to unwind, the weight transfer moves to the left pulling the arms through with the body. The momentum of the arm swing helps to pull the body around into the finish postion.
One of the best drills to feel this move is the step into the ball drill or baseball swing drill( swing your club to the top of your backswing, pause, then pick up your left foot and take a step forward and once your foot hits the ground the arms should swing through). The proper weight transfer is a critical move in golf, so much that players should practice it until it is a natural move. When starting your backswing, pay close attention to your footwork and also that right leg. Keep the right leg/knee flexed so it will act as a stabilizer. This will help you to rotate your hips only so far, allowing your body to coil to create power. Just remember to maintain the platform with the legs and feet so you can keep your balance.
Once you complete your backswing and your weight is over your right leg, you are then ready to release the coil, keep the platform as you strike the ball, and finish your swing by the continual rotation of the hips to the left. The transfer of weight from the right leg to the left is the foundation of the proper footwork. Unless the lower portion of the right leg is braced, the movement to the left will be flawed. Your finish will tell you if you have made the correct transfer as your hands and arms should finish over your left shoulder with front of your body facing left of the intended target.
Being able to move the weight from right to left(left to right if you are left-handed) is a priority on the scale of the principles of the golf swing and that it is highly recommended to practice this thoroughly until it is accomplished at an efficient level.
Again, using the legs properly does three vital things in the golf swing:
1) provides the platform for the rotation of the body and swinging of the arms
2) adds impetus to the movement
3) places the body in a position to strike the ball with the clubface traveling in the right diirection and at the correct angle of approach down to the ball.