As a global, user-supported project, documentation for TYPO3 exists in many locations (and, thankfully, in many different languages). For the answer to most questions look first to the central TYPO3 Document Library where you will find several useful tutorials, and guides to installation, configuration, and getting started with TYPO3.
The Getting Started tutorial is based on the Introduction Package and is the number one resource to get you on your way with TYPO3. The Getting Started tutorial’s permanent URL is: http://typo3.org/documentation/document-library/tutorials/doc_tut_quickstart/current/

TYPO3 Wiki

Find additional documentation in the TYPO3 Wiki, which provides how-to guides conveniently classified for different types of TYPO3 users.

• Editors can find documents on how to handle and manage their content.
• Administrators can find documents on how to manage security, users, and fine-tune performance.
• Developers can find how-to guides to get started in creating their own TYPO3 extensions.

TYPO3 API Documentation

The TYPO3 source code contains abundant internal documentation, which will allow developers to understand many functions and features just by browsing through the various classes and methods. Because TYPO3 uses JavaDoc style documentation, it is possible to automatically create a complete documentation of the TYPO3 core.

Additionally, the TYPO3 Core APIs manual from the Documentation Library describes important components of the API, and gives many examples how to use it.