Qualifications
Unless you're truly a super-genius (and not the Wile E. Coyote type), to be a database administrator you'll need a bachelor's degree in a computer science field, excellent problem-solving skills, and to be a wiz with both software and hardware. Some on-the-job training is also a necessary part of becoming a full-fledged DBA.
Make sure to take advanced math classes in high school. In college, aim for majors like computer information systems, management information systems, or computer engineering. A few colleges have a specific database administration major, but you're still likely to take a lower-level computing job before working your way up to database administrator.
The cost of getting a computer science-related degree varies depending on whether you go to an in-state or out-of-state program and whether you choose a public or private college. In general, a four-year degree will cost you anywhere from $80,000 to $184,000 (source). It really pays to check out costs when deciding which college to attend.
What other qualities do you need? Database administrators need to be very detail-oriented and have excellent problem-solving skills. You should also be able to work in a support role and maintain a strong sense of integrity in your oversight of personal, sensitive data. DBAs must also work well with various departments in order to structure data in the most user-friendly ways, so listening skills are vital.
Database administrators need to be committed to life-long learning as technology grows and changes. In some cases an advanced degree or certification in database administration software can help advance your career.
Remember, knowing what not to do is just as important sometimes as knowing what to do. We'll refer you back to Wile E. Coyote. Learning what not to do wasn't his strong suit.