Graphene builds on top of Selenium WebDriver project and brings extensions which helps you write robust Java-based tests simply from your IDE.
Graphene is thus not standalone project, but extension over Arquillian and Selenium projects to make the testing easier.
You can start with resources Introducing WebDriver and WebDriver's Advanced Usage.
After getting yourself familiar what WebDriver is, you can dive into Graphene documentation.
If you won't find resources how to achieve something with Graphene, let's try to look how to achieve that with WebDriver.
Graphene helps you to bring your test project to the world of Arquillian as well as brings very useful addons.
However you can use as much Graphene as you want, since Graphene integrates with WebDriver non-pervasively.
The integration starts with instantiation of the WebDriver instance leveraging Arquillian Drone extension.
Graphene then takes new instance of WebDriver's browser session and store it in its context.
The Graphene also wraps the WebDriver instance in order to intercept calls.