I got my start by accident. I was a Application and Business Analyst that ended up needing to query the database to find the scope of a problem and eventually landed in a Developer Position because I got fed up waiting on my projects to be scheduled by Developers and started writing the code fixes myself. I worked as a developer for 2-3 years before making the transition to DBA for the next 2 years and then to Sr. DBA after that. All my experience was trial by fire though, and I don't necessarily recommend that for someone just starting out. If you've never messed with a cluster before and you have to immediately handle a problem with a Windows 2000/SQL 2000 cluster, you could be in the position to be doing an "Update Resume, Contact Recruiter" task if you mess up. That's a lot of pressure to be under out of the gate. The best thing would be to find a Dev or Jr DBA position that may involve working under someone who is less educated and less knowledgeable about SQL than you may currently be, just to get the experience. It sucks but at some point everyone had to pay dividends.
Brent Ozar has some good blog posts about this subject as well:
How to Get a Jr DBA Job - Part 1[/url]
Part 2: You CAN Get DBA Experience Without a DBA Job[/url]
Part 3: Getting DBA Training On the Job[/url]
Also look at his interviewing category. It's quite large and has a lot of good information for people aspiring to become a DBA.