sterndata on "Update MySQL for dummies?"

Hi, I've recently been getting MySQL errors on my wp login page. That isn't the problem. The problem, as I have been made aware in researching said errors, is that my MySQL needs updating to MySQLi (or PDO).

So I know I need to update it, but basically I don't know how. And anything I've googled assumes a certain body of knowledge that I simply don't have, and is missing the earliest steps.

I basically don't even know what MySQL is, what it does, where it's located, which files are driving it etc. I just know it needs updating to be secure. So could somebody please provide or point to a step by step guide for beginners? I'm sure others will find it useful too.
Thanks.