To sit in seiza, a person kneels with their legs folded underneath their thighs and their buttocks resting on their heels. The knees should be approximately two fists' width apart for men (or sometimes wider in karate) or close together for women. The hands should be mid-way down the thighs, either flat or cupped (if ready to draw a sword), resting naturally.
Whilst sitting, the back should be straight the elbows by one's side. The tops of the feet and toes should be flat against the floor. Occasionally it is said that the right toe should overlap the left toe.
There are various methods to assume seiza depending on the formality and context of the occasion. In aikidō and iaidō, the following method is appropriate.
Keeping the back straight, begin to bend the knees to lower yourself to the floor. If wearing a hakama, move the palm of your right hand down the inside of your right thigh and gently knock the hakama first to the left and then to the right. Lower yourself onto your left heel, and then your right heel, sinking into position whilst maintaining zanshin (mindfulness) and good posture.
Rising from seiza
Push forwards from the hips and come up onto your toes. Raise your left foot, putting it in front of you with a 45 degree bend in the knee and, using it to support your weight, push up with your left leg to raise your right foot to meet with your left foot. Your hands should come to rest by your sides.
Do not lean forwards unnecessarily or lean on your knee for support as you stand as this represents bad form. Maintain zanshin and stand with one controlled, fluid motion.
I have heard it said that when in the presence of a kamiza, one should rise using the foot closest to the kamiza in order to avoid 'exposing' oneself to the kami or respected figure. However, this does not appear to be a universal consideration.
Kiza (跪座) is a position similar to seiza in which one rests with his or her toes propped up rather than rested flat against the ground. Suwariwaza is performed from kiza (to enable mobility), as well as some cuts in iaidō in order to avoid spraining the instep from jumping up directly from seiza.