I took a class in SQL Server about twelve years ago which lasted a few months. It was a part of a larger certificate program in client-server programming. The course I took covered querying… and that was about it.
However, there is MUCH more to databases than simply knowing how to write a query. There is database administration, database development, analytics, business intelligence, data mining and on and on. You may want to look into these various fields and decide what aspect of it you want to go into. The amount of time you wish to devote to this is strictly up to you — but keep in mind that, like most any other endeavor, the more time you put into it, the better you will be at it.
The Wolf