Moving MyBB - from Shared Hosting to VPS

I need to migrate a secondary forum from shared hosting to VPS running CentOS 7 but I've never done it in past.

Can you recommend me to a good guide for that?

There's no difference in MyBB side, only in server side. So, you don't need a "MyBB Migration Tutorial", only a VPS tutorial about how to configure it. DigitalOcean have good ones in their help section about VPS management.

just copy the files and database, thats all you need todo. The rest is basic web admin stuff.