Many foreigners working in China use Chinese names to get around, esp. those in Hong Kong. They think in that way, those Chinese people who speak little English can remember their names much easier, facilitating business opportunities.
1. You should know something about how Chinese people get their names. Most people (Han nationality) put their surname first and given name last. Most surnames only have one character, but some can consist of more than one. The surnames are handed down generation from generation, and in some large clans, even the given names have a pattern. Check some Jia Pu (records of the family tree), and you'll see brothers and cousins of one generation has one common character in their given names. And those characters can even form a quote from a book or a poem.
2. You should know how Chinese people pronounce your name in their native tongue. Unlike Japanese people, which use Katakana to spell out foreign names, Chinese has its unique system of translating foreign proper nouns. They use characters of the similar sounds. Unfortunately, there are many homonyms in Chinese. So the process of assigning Chinese characters to your name can sometimes be arbituous. There is, however, some standard ways of translating foreign first names. If you tour Chinatown in San Francisco or visit any souvenir store in Hong Kong, you can get a key ring with your first name in Chinese characters. For example, if you are called "Stephen," you can get a ring for yourself, with Chinese characters read as "shi (history) ti (upgrade) fen (fragrance)". The meaning has nothing to do with your first name. For family names, things are really complicated. Mainland China, Taiwan, and Hong Kong have their own distinct ways of assigning certain characters to certain names. So it's not surprising to learn that Bush is "bu shi" in mainland, and "bu xi" in Taiwan. Kerry is "ke li" and "kai rui", Putin is "pu jin" and "pu ting". That can be confusing.