How could relaxing reduce pain? Well, the uterus is built of two opposing types of muscles: longitudinal muscles, which run vertically down the top of the uterus; and horizontal circular muscles, which form the lower half of the uterus. During labor, the longitudinal muscles contract to move the baby down and out, but if a woman tenses up, the circular muscles lower down "close the outlet, maintaining the uterus in its unemptied state. ... Then the muscles that empty the uterus and the muscles that hold it closed are working against each other" (Childbirth Without Fear, Grantly Dick-Read, M.D., p. 67) and pain results. Just as it can become painful when the bladder needs to be emptied but the timing isn't convenient, so there is unnecessary pain when half of the muscles of the womb are trying to clear out the uterus but the other half are tense and constricted.
Therefore, the key to greatly reducing labor pain is to learn to relax the whole body deeply. It is good to begin practicing this as early in pregnancy as possible. Find a quiet spot, and lie down. Get in a comfortable position where you don't feel like you have to use any muscles to support yourself and you can completely let go. Then, methodically and very slowly tense and release your muscles one at a time, from your toes all the way up to your face, consciously noting the difference between tensed muscles and relaxed ones. The face is a key area to relax because "if your mouth is tense, you will be tensing the pelvic area, too" (Ibid., p. 73). As you enter this relaxed state, take deep breaths to allow extra oxygen to reach the uterus. It is a good idea to practice this deep relaxation on a regular day before going into labor. Then your body will be used to how to relax when the time comes.
Ina May Gaskin, in her book Ina May's Guide to Childbirth, recommends blowing "raspberries" or "horse lips" to effectively relax the mouth (and therefore the cervix as well). To do this, completely relax your lips and blow a good amount of air through, letting your lips flap lips together.
Relaxing into the pain instead of resisting it will allow your body to do what it is designed to, with the least discomfort possible. When immersed in the intensity of labor it can be challenging to get back to that place of relaxation. This is one reason why a doula can be vital as a labor coach and even help you have a less painful birth.