Because the Chinese (Han) script is largely logographic, its characters do not correspond directly to the phonemes of the spoken language. As a result, the process of romanization (or indeed transliteration into any other script) does not employ the same kind of character substitution employed when transliterating from an alphabet or an abugida, for example. The process of romanizing Chinese is complex, and some Sinologists have identified over 50 systems for this purpose (from 1994, Warren Shibles, Chinese Romanization Systems: IPA Transliteration).

The most common system by far - and the international standard - is Hanyu Pinyin. This is an indigenous Chinese system created in 1958 by the Association for Reforming the Chinese Written Language, in order to transcribe the Chinese language phonetically. Prior to this, the Gwoyeu Romatzyh system had been devised, but this was never widely adopted. (Another popular indigenous system, which, while not a romanization system, also serves the purpose of representing Chinese phonetically, is Bopomofo. This consists of small Zhuyin ruby characters written alongside the Chinese as a phonetic gloss. Bopomofo is widely used as a pronunciation guide, especially for children and foreign students of Chinese.)

There have also been a number of romanization systems created outside of China, although modern works tend to use Hanyu Pinyin except when quoting from earlier texts. The Wade and Wade-Giles systems were developed in Britain in the 19th century; the former had the disadvantage of not indicating tone, but this was resolved in the latter. These were quite widely used, but required a number of special characters which were often omitted, meaning that accurate Chinese pronunciations could not be reliably deduced from the Roman texts. Almost 100 years later, the Yale system was devised at Yale University in the USA. This system was created originally to facilitate communication between Chinese and American military personnel during World War II, but came to be widely used in academic contexts also.

For further information on this topic, Wikipedia provides a good starting point:  https://en.wikipedia.org/wiki/Romanization_of_Chinese. Each of the main Romanization systems also has its own page on the site.
The University of Massachussets has also compiled a useful resource, including a set of tables comparing the way that Chinese syllables are romanized under various systems:  http://www.umass.edu/wsp/reference/languages/chinese/romanization/.
The International Standards Organization has published a paper relating to ISO 7098 (Pinyin), which explains the principles of Pinyin romanization and includes a table of syllabic forms. This is available for purchase from:  http://www.iso.org/iso/home/store/catalogue_tc/catalogue_detail.htm?csnumber=13683.