The source is the documentation! (General wisdom)
The TYPO3 APIs are first and foremost documented inside of the source scripts. It would be impossible to maintain documentation at more than one location given the fact that things change and sometimes fast. This chapter describes the most important elements of the API. Some other elements have their own chapter further on.
In general the TYPO3 Active Contributors Team and all contributors aim to produce well-documented source code. As such the best way to look up a particular class or method is to use the online API browser at http://api.typo3.org/.