One of the best ways to learn how to do anything new (including software APIs!) is to get your hands dirty as quickly as possible. These examples will show you how to perform tasks ranging from something as simple as applying DataTables to an HTML table, right the way through to doing server-side processing with pipelining and custom plug-in functions.
Please refer to the DataTables documentation for full information about its API properties and methods.
Additionally, there are a wide range of extensions and plug-ins which extend the capabilities of DataTables.