I am going to focus on one neglected part of supporting, which is the pelvic musculature. From the anatomical point of view, this support comes not only from the gradual contraction of the abdominal muscles (both the recti in the front and the obliques on either side), but also a sustained level of tone in the muscles in the floor of the pelvis—these are the muscles which lift the pelvic floor and also control the sphincters involved in excretion. (These incidentally are the muscles that are strengthened by the Kegel exercises prescribed by the obstetrician.)
The Toothpaste Tube
Simplistically, think of the expelled breath (which flows past the vocal folds and powers the voice) as toothpaste, squeezed out of a tube. You can of course squeeze out the toothpaste like kids do, by grabbing the tube in the middle and forcefully closing your hand. But this is not the best way to get toothpaste out- it pushes only some of the stuff up through the nozzle. Much of the energy is wasted in pushing the paste down the other way, toward the crimped end of the tube. To get every last bit of the toothpaste out of the tube, you need to squeeze beginning at the bottom end of the tube, pushing all of the paste toward the nozzle, in a gradual and controlled fashion.
Breathing with Less Muscle Effort
Grabbing in the middle and squeezing corresponds to abdominal breathing with no support: it wastes muscle effort, lacks control, and only partially empties the lungs. Contracting the abdominal muscles without pelvic floor support will push the abdominal contents in both directions- up (against the diaphragm, expelling the air from the lungs), but also down. Pushing down is useful when going to the bathroom or giving birth, but not for singing!
The key to good support then is to maintain a degree of resting tone in the muscles of the pelvic floor while exhaling. This directs the force of abdominal muscle contraction upward, allowing for maximal controlled emptying of the lungs. Musically, this translates into singing with less muscle effort, the ability to sustain the voice for longer phrases, and also better control of sound intensity.
-Anthony F. Jahn, MD, FACS, FRCS(C)
This discussion is for general information and not to be construed as specific medical advice that you should obtain from your own physician.

Dr. Jahn is an internationally renowned otolaryngologist based in Manhattan with a sub-specialty interest in the professional voice. His practice includes classical and popular singers. He holds academic appointments at Mount Sinai School of Medicine and Westminster Choir College in Princeton. He is Medical Director at Jazz at Lincoln Center, and former Director of Medical Services at the Metropolitan Opera in New York. Dr. Jahn has published several books for vocalists, including “Vocal Heath for Singers” (Singdaptive) and “The Singer’s Guide to Complete Health” (Oxford University Press).