Making changes to a WordPress Database

Hi, I've been doing research on how WordPress and BuddyPress actually work. I've made a lot of progress with the help of MANY here in that, I've gone from seeing WordPress as a kind of "Black-Box" to understanding how Themes and Child-Themes work. However, my next step is understanding how the Database that holds all the data works.

Lets assume I wanted to add a new function to my brand new theme that keeps track of something specific related to data. I'd have to manipulate the database...correct? So, how is that done?

How do I manipulate the current data and how do I add a Field or Table to add new data that is not part of any current plug-in?

Thanks for your help,
Fulano