An illustrated technical explanation of how the sacroiliac joint works: http://thelowback.com/how.htm
Exercises you can do yourself at home to fix a subluxation: http://thelowback.com/fix.htm#exercises
The site has simple drawings illustrating each of the exercises below:
SELF-TRACTION SUPINE The patient can use traction for self-correction by pushing the thigh toward the foot hard enough to lift the buttock on that side. Lifting the head at the same time will enlist the abdominal muscles. Repeat several times on each side alternating sides each time.
SEATED PATIENT CORRECTION may be done while at a desk or in a car. Push one knee out. Pull the other knee back firmly to pull the pelvis down in back. Tighten your abdominal muscles to pull the pelvis up in front. Do several times on each side alternating each time. Repeat several times daily.
STANDING PATIENT CORRECTION Tighten abdominal muscles and push the knee toward the floor. Repeat on the other side. Alternate exercise several times on each side. Repeat correction several times during the day.
DIRECT PATIENT CORRECTION The patient can self-correct any time during the day no matter what position he happens to be in at the time. Just by pulling the knee into the axilla or bringing the axilla down to the knee. Stretch firmly several times on each side, alternating sides each time.
ISOMETRIC CORRECTION Grasp the knee with both arms, hold firmly and push very hard outward with the knee. Be sure to tighten the abdominal muscles while pushing with the knee to enhance posterior rotation of the pelvis and when lowering your leg.
STRETCHING THE CORE MUSCLES ON THE ASYMMETRIC PELVIS As the core muscles are most active during normal gait when the pelvis is asymmetrical, they are most effectively stretched when the pelvis is asymmetrical. Seated, project one thigh and retract the other to create an asymmetric pelvis. Flex and twist your trunk toward the side of the retracted thigh. This stretches the piriformis, the sacral origin of the gluteus maximus, the quadratus lumborum, the multifidus, the abdominal obliques, the latissimus dorsi and others. Repeat toward the other side.
STRENGTHENING THE CORE ON THE ASYMMETRIC PELVIS USING MUSCLE ENERGY TECHNIQUES In order to strengthen the same muscle groups, retract your right thigh and project your left. Twist trunk to the left and grasp the right leg with the left hand. Now extend and rotate the trunk to the left while projecting the right thigh and retracting the left. Provide resistance to the trunk rotation with the left hand. Repeat on other side.
MUSCLE ENERGY EXERCISE FOR THE CORE ON THE SYMMETRICAL PELVIS Strengthening the rectus abdominis and the abdominal oblique musculature is necessary to help maintain posterior pelvic rotation throughout the day. This exercise is done on the symmetrical pelvis. Place both hands on the same knee, tighten your abs and pinch your buttocks tightly together. Push down hard on that knee for several seconds. Repeat on the other side. Do five times on each side.