What are the necessary course requirements to become a DBA?
I've discovered my education as a DBA and as an IT professional came in three tiers.


What I learned on my own. Basically from each job I was hired for, I learned how each shop operated, listened to business requirements and learned on my own how to complete the assignments. A lot of reading the manual (now Googling) and trial-and-error is involved but it's ultimately how we all learn. 
What I learned from certifications. One time I picked a textbook for my favorite programming language and discovered that I was only using a fraction of the techniques described on the job. I wanted to learn as many aspects as I could. In the back of the book they had mentioned the certification program for my language (Microsoft Certified Professional in this case). It's a structured way to learn all the major features of the platform you're focusing on for your employment. There's a lot of studying and practice involved (My MCSD took four tests and my MCDBA and MCITP:DBA were comparable). You'll learn about features you might not end up using on a particular job site, but being aware of their existence helps shape you decisions on how to tackle a business requirement. 
What I learned from the community. This by far, is the most valuable. You learn firsthand that you're not alone in your profession. You also learn what your peers have learned on the job and through their own research, and it's great to share what you've learned. You'll find your mentors here as well. There's a large of community of masters, MVPs and fellow DBAs who share their knowledge in-person, in print and online. Search for them in Google, attend a local user group, have your employee fund a trip to your favorite products' annual convention. I've seen at SQL PASS twice and the knowledge shared there is amazing.


One book that I've personally found best describes the calling of a DBA is DBA Survivor: Become a Rockstar DBA. It goes beyond the technical and talks about your relationship to your customers and your responsibilities to the tradecraft. It helped reaffirm my belief that the DBA profession is an essential one that is challenging, honorable and rewarding.