You can improve upon the basic crawl by changing your body position and using the arms more.
Keeping your chin tucked in close to your chest will help to improve speed.
Keeping your head still will also increase your speed through the water.
Some coaches will put a pound coin on your forehead to see if you can keep it there for a whole length.
Letting your shoulders and hips roll slightly will help to keep your body streamlined.
When you put your hand in the water, lean towards it with your shoulders and hips.
You can help achieve this by letting the opposite shoulder lift as your hand leaves the water.
Even when you are rolling, you should be more on your back than your side.
Keep your legs close together throughout the stroke using the long shallow kick described in the basic back crawl.
If you imagine being able to feel your knees and big toes touching as they kick, this should help.
The way you use your arms will make a real difference to the power of your back crawl.
Use the alternating action described in the basic back crawl, bending your elbow and pushing your hand towards your feet.
You can improve this action by bending the elbow more so that the hand is close to the side of the body.
Pointing your elbow down towards the bottom of the pool will ensure your hand is doing most of the work and give you a stronger pull.
Lifting your hand out of the water, with your palm facing your leg (thumb first), turn it so the little finger will go into the water first.
Keep the legs moving all the time and the arms following each other. Breathe in every time your left or right arm goes over the water.