So, you've spent some time playing with the IDE and tried your hand at a 'Hello World' app.
You could study the documentation? But a more interactive way to explore the API is to load the Kitchen Sink project.
Appcelerator provide both a Desktop and Mobile versions of a Kitchen Sink app on the popular GitHib site. Just download the zip, extract the contents contents and Import the project file into your IDE.
Inside you'll find host of useful code examples that exercise different part of the API. These can be copied to other projects as is, or modified in any way you wish to customise the app behaviour.
Although it's an excellent starting point, it only covers a small fragment of the complete API. So, you'll have to dive into the online documentation from time to time.