The word "de" is used in the Chinese language for three different particles. They are written with three different characters, but are all pronounced that same way. These words are some of the most common and most useful words in the Chinese language, and the first "de" is probably used more then any other word in Chinese.
The three words are all part of the vernacular Chinese, a style of Chinese dating back to perhaps the Yuan Dynasty (around the 13th century), and for many years widely considered to be somewhat low class, although many great works of literature were written in the vernacular. Thus, for many years, serious academic scholars looked down upon the usage of "de" and its exact usage was never quite made clear. In addition, about 10 different characters were used to write it. The closest analogy to English would be if scholars who wrote all their papers in Latin had never bothered to describe the grammatical difference between "s" for a possessive and "s" for a plural, and sometimes used different letters to define the same sound. However, with the advent of the baihua movement this century, which made vernacular Chinese the language of academics and literature, the seperate meanings of "de" and the different characters for each were standardized.
The first "de" is used as a possessive, and to link adjectives to nouns, and by extension, to change adjectives into nouns. This word is the most common, and most helpful of the three. The simplest usage of it is in parallel to English possessive "s", in such sentences as Zhe shi ta mama de shu, "This is his mother's book" or Zhe shi wo de che, "this is my car". However, even with this simple usage, it is not always straightforward, since unlike the possessive, this particle is not always required. Especially in phrases where the connection is assumed, the possessive "de" is not needed. For example, it is not neccesary to say wo de baba "my father", because the connection is apparent. However, it would be neccesary (probably) to say wo de daifu "my doctor". However, this "De" is not used merely as a possessive. It is also used more broadly to link adjectives or descriptive phrases to nouns. For example, hong de pingguo would mean "red apples". Of course, this phrase would not often be used, since hong pingguo suffices. However, a phrase such as zuo gonggongqiche kan shu ren "riding the bus reading book people" could better be parsed by adding the "de" and turning it into zuo gonggongqiche kan shu de ren, which seperates the adjective phrase from the noun it modifies. By further extension of this, "de" can be used to transform adjectives into nouns. For example bai de dongxi would mean "white things". However, the noun can be removed, leaving only the adjective and the "de", with the fact that it is pointing at some noun implied. This is actually a good technique for people learning Chinese, who have a limited vocabulary: simply refer to something by its color and add the "de".
The second "de" is used to modify verbs. It describes the degree or manner in which that verb is performed. For example, chi de hen man means "eat very slowly"; and pao de kuai means "run very fast". These are short examples, the phrase put after the "de" to describe how the verb is being performed can be quite long, such as ta xing de tai chidao, ta bu shang zao gonggongqiche, jiu bu keneng shang ke , "he woke up so late, he didn't catch the early bus and couldn't attent class", with everything after the "de" being used to describe exactly how he woke.
The second "de" is also used in verbal compliments, set phrases that describe whether a verb reached its expected conclusion. For example, in Chinese, it might be said a door was kai de kai, "opened to the state of being opened", meaning the verb "opening" was undertaken until the door had reached the adjective state of being "open". This sounded strange to me at first, until I realized that the English equivalent was to say a door was "opened up", which actually makes less semantic sense then to say it is "opened open". In any case, the "de" in a phrase such as ting de jian means to "to listen to the point of perceiving". This verbal "de" actually uses the same Hanzi as the classical Chinese verb for "to obtain", which means that it perhaps is a regrammaticalization of that verb. shou de qingchu "speaking clearly" could be seen to be a way of saying "speaking in a way that obtains clarity". However, that is mostly an academic point.
The third "de" is used to turn adjectives into adverbs. Chinese, whether classical or modern, traditionally has very few adverbs, perhaps two dozen, and they are always placed before the verb they are modifying. They are usually fairly simple words, such as bu, dou, ye, equivalent to English "not, all, also". Of course, somewhere along the line, someone decided that they wanted to say things more fun then tamen dou zuo and thus they invented the third "de" so they could turn any adjective that they wished into an adverb. Thus, they could make more versatile sentences such as Tamen gaoxing de zuo, "they happily walked". Often, for whatever reasons, the adjective is doubled when used as an adverb, so the phrase may be phrased Tamen gaogaoxingxing de zuo. However, not all adjectives can be used with this "de", and overuse of it may be considered poor literary form, even in spoken Chinese.
That, then, is the three particles pronounced "de" in Chinese, that, while very complicated to explain, make speaking much more easy and versatile.