I was getting started with a project with Libgdx and my idea was to make a procedural game, but I've never approached this topic. I'm very curious and eager to learn, do you guys have any idea where I could start?

While I have no specific recommendations about how to go about it, I do remember a game I loved: Adventure Construction Set

You could make adventures yourself or let the computer spit-out an entire adventure after it spent about 1 hour doing its thing. All the more amazing is that it ran on the Commodore 64, a 64k machine! There's a ton of nostalgia for it on the web. Walk on over to Google for some ideas.

Something that works great is noise. Use it for terrain, for building placement, for quest placement, for all types of different things. To make it fast, that will take some work and tweaking towards your particular case. For example, I use modified perlin noise to create terrain, biomes, and even creatures! There are tons of things easily reached from google or gamedev for how to use, make, and apply different types of noise.

-ST