In addition to @Sir_Cmpwn's answer, the developer logs from Voxel Quest (@gavanwoolery on HN) and Seed of Andromeda are both excellent starting points for getting a general overview of what's involved in this sort of undertaking. Both of those games ended up releasing their full source code by the way, so you're also free to pick through every last detail if the logs aren't enough.

Links:

https://www.voxelquest.com/news/every-version-of-voxel-quest...

https://www.seedofandromeda.com/blogs

Ah, then some useful algorithms and keywords to study would be OpenGL, voxel rendering, A* pathfinding, cellular autonoma, perlin noise, etc.

Red Blob Games has a lot of good articles covering many of these subjects, here's a few:

https://www.redblobgames.com/pathfinding/a-star/introduction...

https://simblob.blogspot.com/search/label/noise

Creating Minecraft is a lot of work, but creating something that generates psuedorandom worlds and lets you walk around them is a feasible couple-of-months-of-spare-time sort of project, assuming general programming competence but not assuming any particular skills in computer graphics. Odds are good you can find someone blog posting about it in your favorite language if you look. I've seen a number of them. If you cheat and use the Minecraft textures it looks a lot like early Minecraft too.