I started work as a database developer. Back then we did everything. You did the modeling, the physical structure, capacity planning, backup and restore planning, ETL, report writing, application development, the works. We didn't even have a name for DBA, Data Analyst, Modeler or ETL. We were programmers and programmer/analysts.
Everything except Cobol I've learned on the job. Believe it or not, I started out as a secretary over 20 years ago. The only educational training in IT that I had in school was a class in Cobol. I taught myself everything else, some of it on the job, some just learning it on my own.
I went from Administrative Assistant to Sr. Programmer/Analyst all at one job and learned everything there was to being a DBA and a database developer over a five year period. The step from DBA to Data Modeler and ETL was not even a step. I already knew it, but we called it Migration. Learning the new buzzwords for what you already do is a key to getting ahead. In fact, I was already an Enterprise Architect. After several years, I managed to get a consulting job that taught me Data Warehousing.
What it takes is an ability to learn new things quickly and enjoy it. The training out there is still ridiculously expensive. Some companies still want an Oracle Masters or it's equivalent. Who can afford it unless their company pays for it?! My educational background is several years of college but no degree. I've never really needed it. There was a point where it kept me from getting the wages of my peers, but that was long ago.
Bottom line, learn everything you can about databases and data warehousing. Read everything you can get your hands on. If you can't learn or use it at your present job, download anything you can find online and start building something for yourself. Oracle's Tech Net is awesome. Read Kimball's Data Warehouse Toolkit.