The documentation you were looking at might’ve been the Matrix specification.

There is documentation on how to host a Matrix server, I’d honestly recommend using containers (maybe docker compose) for this one. It can definitely be confusing setting up a service like a Matrix homeserver for the first time.

As for other people finding it, you can (and should) make your homeserver invite-only. It’s also possible to disable federation, which makes the server self-contained. It will not accept incoming connections from other servers, nor make outgoing connections to other servers.

This does mean everyone you want to talk with has to be on your homeserver. There are probably better options available if you want to avoid Matrix’ federation issues, like Spacebar.