Most languages share a similar set of greetings. Those general welcoming messages include Hello, Good morning/afternoon/evening, goodbye, happy new year and so on. In most cases these expressions are quite short, easy, and neatly matched with English equivalents.
Chinese, an Eastern language, has these common traits as well, and I am pretty sure you can master the expressions of greetings above within just a few hours. However, Chinese, and the eastern culture behind it, offers a group of special greeting expressions quite different from those in English.
For example, Chinese greetings can be very personal and may sound annoying for English speakers. One may ask whether you have had a meal yet (吃了吗？) or the place you are heading for (去哪儿啊？). Requesting personal information is also common such as asking a person's age or commenting that they've gained or lost weight. (您贵庚啊？). These questions regarding personal information seem quite rude to westerners, but are a symbol of closeness for Chinese. So, be bold enough to greet your Chinese friend with "吃了吗" and he'll probably reward you with closer friendship.
Another interesting thing about greetings are the expected answers. Basically, small talk greetings are not expected with a very specific response. When you ask "去哪儿啊", you don't need to report your destination in detail, but just a very short "going home (回家)", "going for lunch (去吃饭)" or "(visiting relatives) 走亲戚" will suffice. Moreover, some common expressions of greetings may not have perfect equivalents in English. One example is that the response to "谢谢", or "Thank you" is "(you are welcome)不客气". This is slightly different from the English "you are welcome", since literally the host is blaming you for being too "guestish", being not close enough to the host. So we could see in Chinese the sense of closeness must be achieved in greetings -- at least through the text itself -- and that is something quite unique and lovely in Chinese culture.