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.
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.