If you are new to Octokit, I recommend reading the Getting Started guide, which walks through configuring the basics.
When you're done with that, have a look at the topics listed under Features to get an idea of what other things are available.
If you're looking for some real-world examples, check out the Samples section.
There's also some advanced topics which require familiarity with the internals of Octokit. You shouldn't need to know these well, but they're there if there comes a day when you do.
If we still haven't covered a topic you're interested in, check out the suite of integration tests which can help you to get familiar with how things currently work. Then open an issue against the repository, so we can properly document things.