Bowing is an important part of any martial arts training. By bowing you are showing courtesy, respect and gratitude to your art, dojo, sensei, other students, and yourself. There are many situations in which you should bow. You should bow:
For a standing bow, bend forward at the waist about 30 degrees keeping your back straight. When bowing before practice keep your eyes up looking forward. As you bend forward your upper arms stay next to your body and your forearm comes up parallel to the ground, hands in fists. When bowing in receipt of an honor or complement, your head and eyes should be down in humbleness. As you bend forward your hands slide to the front of your thighs.
It is also important to remember that the very nature of our practice violates one of the prime tenets of self-defense: you are allowing someone to get close enough to attack you or even to put their hands on you. By bowing you remind yourself and your partner that this is a special case, that this is practice.