How would you track DB storage use and then extrapolate it? I need to track the size of various DBs we have, then see it's growth rate so that we can guess where it will be at certain times. I'm using Oracle 11g first, but will eventually be applying this to other DBMSs like DB2 and Sybase.

I'm not even sure where to begin or what commands/queries I'll need to run.
You just need to start by collecting data.

There are a few different valid ways of judging the size of the database -- number of rows in each table, size of table and index extents, size of data files -- so first you have to define what decisions you intend to make based on the data. Do you want to know when you'll need to add storage? Or when you'll need to extend data files?