It seems that most of the tutorials use the scenario of a shared database, and emphasize using a different db prefix.

Even though I am just starting out, I know that I want to use separate databases per site.

Is there a tutorial for this case, using the MySQL root credentials, etc.?

In the manual:
It is also possible to force using a specific MySQL root user. This MySQL root user is defined in “multisites.cfg.php”.

I made this edit, but for some reason, it seems that I am not filling in the variables correctly for the db name, user, etc.

Sorry if I missed it. I have been through a lot of tutorials today, and am able to set up new slave sites where I create new databases manually, but want to automate that step.

Thanks,
K

The procedure to share the extension between different DB is the same as tutorial video 16 except the fact that you have to provide different DB and that the MySQL User that you will use to share the extension has enought MySQL privileges to do that.

This latest part that consists to use a MySQL user privileges with enought permission is the key element that is not necessary provided by shared hosting.

So if you have a dedidcated server or at least have the MySQL user root login to access the PHPMyAdmin "privileges" menu then you should be able to manage the MySQL user privilegest to provide the permission between the different DBs.

The simpliest method is to use the root MySQL user that by definition has all the privileges.