How the Language Works
Unlike in English, where words are composed of letters, written Chinese words are made up of characters. Most words are composed of two characters, but words are commonly made up of one, three, four or more. Each character represents a syllable and tone for a spoken Chinese language (except for Chinese languages that have no tones like Shanghainese). Contrary to popular belief, a character by itself does not necessarily have any meaning. Often, though, characters have associated meanings as with prefixes or suffixes in English. Like in English, context greatly affects the meaning and pronunciation of a written Chinese word and character.
Context and Meaning
The character 中 can be used in a number of different words with various meanings. 中文 (zhongwen) is the Chinese word for "Chinese". 中 is associated with China in this context. The word 中国 (zhongguo) is the Chinese word for "China" because it was the "central kingdom." A 中心 (zhongxin) is a center (i.e. a health center). 中美 (zhongmei) means Sino-American, but 中美洲 (zhongmeizhou) is Central America. So, we can see that 中 is associated with both China and being in the middle of something.
But it gets even more complicated. When 中 is placed at the end of a prepositional phrase, it can means "during" or "within." When used as a verb, it is associated with hitting as with 中断 (zhongduan, to hit) or 中毒 (zhongdu, to poison). Thus, it is clear to see that 中 by itself has little meaning. Characters have an associated meaning that context violently affects.
Other characters have no associated meaning by themselves at all. For instance, 可 (ke) has no clear meaning. It needs to be used in concert with other characters to produce any meaning at all.
Additional characters have no meaning or shed their meaning because they and are used for names. 布什 (Bushe) is George W. Bush and has no association to cloth which 布 represents.
Context and Pronunciation
When characters are applied to a specific Chinese language (i.e. Mandarin), they usually have a single spoken sound and tone. Context, though, does sometimes affect pronunciation (both sound and tone). The most famous example is 行 which is "hang" in a word like 银行 (yinhang, bank) and "xing" in a word like 行为 (xingwei, behavior).
Components and the Radical
Each character is composed smaller pieces. Some of pieces also have associated meanings and can cue the reader on to the meaning of the word. For instance, most characters with three dashes on the side are associated with water or liquids as with the character 江, which is associated with bridges. Others pieces can cue the reader as to the pronuniciation. There are no hard rules when it comes to character components; exceptions are very common.
Each character has a designated primary component called the "radical." This is used for classification of the character in dictionaries. The stroke number of the remaining components is then used for further classification. Radicals can be difficult to determine, but overtime, a reader becomes familiar with identification. There are a little over 100 radicals that are used for classifying the 5000 commonly used Chinese characters. With the radical and the count of remaining strokes in a character, one can find a character in a dictionary.
Looking Up a Word
Say someone comes upon a word they do not know. For example, 管理. The first thing the reader must do is identify the radical in the first character- 管. In this case, the radical is on the top. The reader would count the number of strokes in the radical. It may not be obvious, but the radical has 6 strokes. One then looks up that radical in a Chinese dictionary's radical index. This particular radical has roughly 40 different characters that contain it. So, the reader then counts the number of strokes in the rest of the character. Again, it may not be obvious, but the character has 8 remaining strokes. There are 6 characters that have both that radical and 8 remaining strokes. This is a managable number to find the character. The dictionary would then contain common words starting with the character 管. The reader would go through the list until they found the proper word.