Here's what I suggest to practice next time your out of the range. Start with the proper address, feet slightly more than shoulder width apart, knees bent, weight distributed evenly accross your feet (not on your toes, not on your heels).
Take the club with your off hand and drop it down into your address position with the entire club head touching the ground. The end of the club shaft should point right at your belt buckle. Now take the club with your strong hand and take your normal grip. Now start your backswing.

Don't sway back, you should turn your hips to a 45 degree angle, which means your back side should also turn 45 degrees. If your backside is pointing directly at the target you've probably over rotated your hips.
Unless you are super flexible, this will not only cause you to over swing, but it can also cause back problems over time because of the torque you are putting on your back. Fourty-five degrees is plenty of a turn.

Once you get to about 45 degrees you begin the downswing by dropping your arms and unwinding your hips.
Once you get the arms and hips in proper sink, you are on your way to creating a very strong golf swing.
Like I mentioned before a large portion of the power in a proper golf swing comes from unwinding the hips through the downswing, but don't overdo it or you'll end up hitting a major hook because your arms won't be able to catch up with your hips.

Just remember 45 degrees is the key, the speed of the hip turn is just something you'll have to work out through practice at the driving range.

The proper golf swing is like a machine. All the parts need to be working together to produce the proper result. Too often I see golfers swing with all arms and no hips. The secret to power is in your core (your hips, legs, back, and abs) not your arms. That's why you don't see too many boby builder types crushing the ball. They lack the the proper hip turn.

If you will focus on getting your hips turned to that magical place of 45 degrees and then let your core control your swing, not your arms you will be well on your way to hitting the ball straighter and further than you ever have in your life. Remember- 45 degrees and then unwind those hips through the downswing.