The field of databases is quite big.

You have 3 main pillars regarding jobs: a DBA (the position Jeff talked about), a database developer and business intelligence.

My personal opinion is that if I ever have to recruit a DBA, I wouldn't recruit someone just entering the field. A DBA's responsability is to take care of my servers and my data, so you trust someone who has been on the streets. Data is one of the most strategic/crucial assets of a company.

The other two functions are more accessible to junior people. Personally, I knew almost nothing about databases, but I was lucky enough to have found a company that took the risk to invest in me, so I became a business intelligence developer. This is something you can do when you're "young", because if a company hires you and invests in training for you, they'll most likely pay you as a junior.