Seiza (literally: “proper sitting”) is a peculiarity of Japanese culture; it is the polite way to sit. Japanese homes are cramped spaces, so there is little clutter (or furniture). Seiza allows people to sit on the floor without lower back pain, while taking up an absolute minimum amount of space.
Sitting cross-legged curves the spine, straining the lower back muscles. The meditating monks who sit cross-legged for hours are actually sitting on the edge of cushions or small benches that preserve their posture.
Seiza is mainly used in the brief opening and closing formalities which bookend each class to help set the right mindset. Much like how one should know which forks to use before going out to a fancy restaurant, one must know the formalities of seiza before visiting a dōjō.
To sit in seiza, sit on your knees, as pictured below. The big toes are crossed. The knees are two fist-widths apart. Your back is ramrod straight, with your chin up, and eyes forward. The hands rest atop the thighs.
[seiza sitting photo]
Your legs will begin to hurt after a few minutes in seiza -- but do not worry, seiza causes no damage. The discomfort comes from stretching underused ankle muscles and ligaments. The best way to avoid the inherent discomfort of seiza is to stretch these muscles and ligaments, and the best way to do that is to sit in seiza -- there's no easy way out. Do not sit in seiza with your toes facing outward. While this seems easier, it stresses the knee ligaments, leading to a crippling injury. Likewise, it is imperative that you only perform seiza barefoot, because shoes will place pressure and strain on your Achilles’ tendon.