What is the correct way of bowing?

The basic way is to lower the head by bending the upper body, standing face to face with the person you're bowing to, leaving a certain distance in between.
The degree to which one lowers one's head differs according to the relationship with the person and the situation.
Women usually put their hands one on top of the other in front of the body, and bow in this way if they are not holding anything in their hands.
If they're sitting in a chair, they stand up to bow.
If they're sitting on a zabuton, or cushion, they move from it to bow and put both hands lightly on the tatami mat or on the floor in front of them when bowing.
It is also necessary to exchange appropriate greetings when bowing, as well as when shaking hands.