You literally sleep nearly a third of your life, so the position you sleep in will directly affect how you feel when you wake up and your physical health. Sleeping positions can affect your general posture and alignment as you expose your body and spine to different twisted or bending positions for a prolonged time, leading to tightness and stiffness when you wake up.
Many people suffer from headaches, neck and back pain, shoulder and hip problems all from poor sleeping habits and positions. Sleeping on your stomach affects your neck and puts it in a compromising, unnatural position for hours leading to neck pain and headaches. The twisting that also occurs through the rest of your spine leads to back pain. Sleeping on your side, even though probably the second best position to sleep in, can cause shoulder and hip problems.
The best way to train yourself to sleep is on your back with a nice comfortable pillow. Sleeping on your back means your body is in a natural anatomical position and does not have increased strains or tension on any part of the body. It does however take a lot of will power and effort over time to train yourself to sleep on your back, especially if that is not what you are used to.