Tutorials
After you have created your very first libGDX project, we highly recommend our A Simple Game and Extending the Simple Game pages. If you’re completely new to game dev and have never developed a game before, this (even more straight-forward) tutorial by tann is also worth a look as an alternative.
From then on, our wiki is your best companion: it provides extensive documentation on nearly every feature offered by libGDX. For any further questions, our official Discord server is good starting point.
There are also many third-party tutorials. A (non-exhaustive) list of them can be found here.
Demos
If you want to inspect some open source libGDX games for reference, this wiki article is the right place to start looking.
The official libGDX organization on GitHub also offers a few demo projects that you can play around with to get a feeling for how to do things. Note that many of these demos have been created during game jams and may not necessarily reflect best practices. To use them setup your development environment, then simple clone the repositories on Github (or click on the “Download ZIP” button of a project’s site) and import the project into your favorite IDE as a Gradle project.