This may seem like a rather simple question, but it is important, and differs from how we address people in the US. In China, hierarchy is an important part of social interactions. That is, who you are and your position in relation to others determines to a large extent how you address them. This is why, in China, that individuals will always exchange business cards when first meet so they know how to address each other.
Terms of address, or how you address someone, depends on your level of familiarity with the person and the formality of the occasion. Below I describe various ways to address people.
1. Surname + title
This is the most formal, and safest way to address someone. In Chinese, surnames always come first. This kind of address is appropriate in all formal occasions and whenever you are addressing someone in a position superior to your own or to someone older than you. For example, if you are a student, and your teacher has the surname 王 wáng, you would address her as:
王老师 wáng lǎoshī Teacher Wang
Or if your boss is a manager, and is surnamed Zhang 张 zhāng, you would address him as:
张经理 zhāng jīnglǐ Manager Zhang
2. Full name (姓名 xìngmíng)
Unlike in the US, it is very common to address a person by their full name. It does not sound strange at all. Even people that know each other well, may address each other by their full names if they are in a more formal setting. Husbands and wives will even use their full names with each other when they are in public. This term of address is common in the workplace among colleagues, as well as at school with Chinese classmates.
You will most likely use these two terms of address with the vast majority of your Chinese contacts.
3. Given name (名字 míngzi)
You have to know someone pretty well to be on a first name basis. This is quite different from the US where you can meet someone for the very first time and refer to them by their given or first name. In China it takes quite a long time to get to the familiarity level to call someone by their given name. This term of address is reserved for in-group individuals, such as friends, classmates, and co-workers that have a similar social status as you.
Just as in the US, nicknames are reserved for those with whom you are very familiar, such as family members, close friends, and close colleagues. Nicknames in Chinese are often given based on physical characteristics, or personality traits. These kinds of nicknames are called 绰号 chuòhào or the more colloquial term 外号 wàihào. Here are some examples of these kinds of nicknames:
小胖 xiǎo pàng “little fatty” for the chubby person
四眼王 sìyán wáng “four eyes Wang” for the guy that wears glasses
书呆子 shūdāizi “bookworm” for the person that always has their nose in a book
A Chinese associate of mine explained to me that her nickname among her friends growing up was 老五 lǎowǔ. This name came about because she had four close girlfriends and she was the youngest. In Northern Mandarin 老 lǎo refers to the youngest member of a group. Since she was the youngest of the five, they used this nickname. You could also use this term for a relative. For example, if you had three uncles, you might refer to the youngest as 老舅lǎojiù or your youngest aunt as 老姨 lǎoyí.
Some nicknames are terms of endearment, and are often a variation of a person’s name and are called 昵称 nìchēng in Chinese. I had a friend who was a bit older than her group of friends so they gave her the nickname, 姐姐 jiějie, “older sister” and called her 冯姐姐 féng jiějie（her surname was Feng). Another friend was named 吴小琪 wú xiǎoqí and her parents and grandparents called her 琪琪 qíqí.
You are quite safe addressing Chinese with surname + title or by their full name. Be careful about using given names or nicknames. Relationships in China form and develop much slower than in the US and it may take quite a bit of time to get on those very familiar terms with someone.
One final note: in the US you will undoubtedly meet Chinese who will introduce themselves with their given name, either their Chinese given name or an English name. What do you call them? The rule I generally use, is that if you are speaking Chinese with them, I go by the Chinese practice of calling them by their surname and title or by their full name. If you are speaking English with them, and they have an English name, go ahead and use the English name. If they do not have an English name, I am uncomfortable calling most Chinese by their given name, even if we are speaking English.