Massage - who would turn down a massage? Not many people, but in labor it is almost essential. Massaging certain areas of the body will help compete with pain messages in your brain for reception (Gate Control Theory of Pain Relief), reducing the sensations of pain, these would be the hairless parts of your body. For example: Hands and feet. While other types of massage, such as effleurage (light, rhythmic massage on your belly), or simple light stroking provide the sensation of companionship.
Breathing - this is what we think of when we think of non-medicinal pain relief measures. A bunch of women hee hee hooing through labor. Breathing is much more than this, in fact, a lot of women never use patterned breathing in labor. Controlling your breathing to be slow and relaxed is more conducive to relaxation and a sense of control over your body. Hyperventilation can deprive you and your baby of oxygen.
Relaxation - it only makes sense that by fighting your body during labor by tensing you will hinder the process and possibly slow your labor, but more importantly it will cause you more pain. It is important to relax and allow your uterus to do the work for you.
Water - is of benefit because it is relaxing, can reduce swelling, pressure and can actually cushion your body from the force of contractions. This is most effective after active labor has begun.
Acupressure - is used to help alleviate tension and to actually stimulate labor by using pressure points in the body, like Spleen Six.
Positioning - can actually relieve pain in a few ways. It can correct a malpresentation of the baby, such as a posterior baby, it can increase blood flow to the uterus, and it can make you more comfortable.
Mobility - this allows your body to move about during labor which enables shifting of your pelvis, etc. It also speeds the labor.
"Special" (Double hip squeeze, counter pressure) - certain measures can be taken for certain situations, for example back labor caused by a posterior baby. Counter pressure is simply putting pressure at the point in your lower back that the baby is pressing on, thus the counter. The double hip squeeze will also provide the counter pressure while also moving the pelvis, hopefully allowing the baby to change to a more favorable position.
Mental & Emotional
Relaxation - this also has a mental and emotional connection. You need to try to concentrate on what will help you through labor. This is not the time to worry about bills, your job, etc. Some women find that visualizations will help them, while others prefer to think of "nothing." Practicing before labor may help you identify which would help you more, but be prepared to be flexible during labor.
Support - being alone can hamper labor by creating tension and fear. Having support from people who care about you is very comforting because you are not alone, and they are doing what they physically can to help you.
This list in not complete. There are many more things that you can do to help yourself through labor, and the ones that I have listed here have only been briefly defined. It is important to you seek additional resources, such as a childbirth class, a doula, or books to help you master these techniques.