I posted my marching cubes tutorial to generate 3D procedural terrains. Marching cubes is an algorithm to generate geometry from math functions. But in game development, we mostly use noise functions here.
A simple approach to generate 3D procedural terrain is to create a plane surface, and modify its vertex position using the Perlin noise. But this approach is not suitable for complex shapes like caves.So marching cube is used. But it is slow and I recommend pre-computing all the meshes and storing them in file. However, you can optimize the algorithm to work in real-time.
To generate huge infinite worlds, we have to generate terrain in chunks. In this way, we generate terrain only around the player and remove the chunk as player moves away from it.
Besides, generating terrain is not the only thing we have to do for procedural level generation. We have tom place objects (such as trees), texture the terrain (using splatmap shaders) and so on. But it starts here.
Link to tutorial: marching cubes.
I hope you will find it helpful <3