That's an extremely open-ended question. The problem is, the daily duties vary from one organization to the next. Further, they vary from one group within the organization to the next. Even further, they vary between individuals within the group within the organization. It has to do with levels of knowledge, areas of expertise, and the general needs of the company you're working for.

Best thing you can do, track down three books, SQL Rock Star by Tom LaRock, Database Administration by Craig Mullins, and How to be an Exceptional DBA by Brad McGeehee.

Read all three. The combination of them will absolutely outline what you need to know.