Improving your swing in general and your backswing in particular is dependent on your ability to execute the fundamentals of the game. When you are building a good back swing, you want to be able to turn your hips fully before you begin your downswing. In addition to working on your swing at the driving range, you can exercise off the course to improve your hip rotation.
Warm up fully before you head to the first tee. Running in place is a very underrated activity because it increases your blood flow and it gets you moving a bit quicker. You don't need to do this for a long time, but three minutes of running in place before you get to the first tee can make you feel much sharper.
Take one of your irons and hold the club behind your back in the crook of your arms. Turn as far as you can to the left and then turn equally as far to the right. Repeat the twist 10 times on each side. This will help promote hip turn on your backswing.
Address the ball squarely. Your left shoulder should be facing the target and your left foot should be directly underneath your shoulder. Your feet should be about shoulder length apart. If your feet are wider than that, you will have a hard time completing a successful backswing because your hips may not rotate far enough. If you stand narrower than that, you may not be able to remain on balance as you swing.
Let your hands follow your hips. You should not concern yourself with your hands on your backswing other than that they should follow your hips and move as your hips rotate to the right. Golfers get in big trouble when their hands lead their swing. Your hips will give you your power and much of your accuracy and they must lead.
Concentrate on getting a full hip turn on the backswing but it doesn't necessarily have to be a hard backswing. You don't want to speed the process because that will upset the timing of your swing. A well-timed hip turn will allow you to rotate fully on your backswing and come through the ball with a balanced finish.
Tips & Warnings
Go at a moderate pace when you take your club back. Power and accuracy come from timing and a full hip rotation and not speed.