People in Japan bow — a lot. It’s their version of the handshake, only more complex, and failing to return a bow is considered impolite. Though it feels awkward at first, it quickly becomes second nature. If you offer your hand for a shake, you probably won’t be refused, but bowing is the preferred method of greeting. Bows also convey apologies and thanks.
While visitors are not expected to know the complexities of the bow, a few tips will help. First, bow from the waist with the arms straight at your sides. Imitate the bows you receive (there are lots of rules regarding the depth of bows — social abstractions that take decades to learn). Don’t overbow or ignore the greeting. It’s better to smile politely and nod your head than to be perceived as rude. After awhile, you’ll find yourself bowing automatically (when I encountered a Japanese coworker at my office in Los Angeles, I automatically found myself bowing in greeting).