I want to become a game programmer, my question is: how?

Program games.

No, seriously.

Be aware that game developers are some of the most overworked and abused devs in the industry. Probably because so many people want to develop games that the companies can get away with it.

Just pick a language and google how to start and then program games my dude.

Don't.

I had that dream when still studying. During the job interview marathon I noticed how bad the environment and conditions are.
Insane hours, constant crunch and horrendous payment.
Even some game devs and a game journalist adviced me against it.

Seriously... Don't.

So I have to change the request in: I want to become an underpaid programmer with unlikely hours an so on....?

Kinda

There are a huge number of courses on the Internet for learning.