Japanese people greet each other by bowing, which has many other functions, such as expressing respect, gratitude, or apologies.
There are different ways of bowing, ranging from a small nod of the head to a 45-degree bend at the waist. Generally, the longer and the deeper you bow, the more formal and respectful it appears to others.
Many Japanese tend to feel uncomfortable with physical contact, although handshaking is becoming quite common is business situations, especially those involving foreigners.
When meeting someone in a business situation for the first time, it is customary to exchange meeshi めいし (business cards) with a small bow. Etiquette guides list a vast number of rules and pointers, but just remember that the important thing is to clearly show your respect when exchanging meeshi めいし.