I'm going to make a couple of assumptions here, please correct me if I'm wrong:

• You're an admin, so you're likely to be interested in learning about databases from an administrative angle, rather than how you can write code to access a database
• At this point, you are more interested in relational databases, rather than NoSQL databases

If my assumptions are correct, I would suggest that you learn by getting your hands dirty. By this, I mean that you should install a database and start playing around with it.

There are many free databases for you to pick from...

• Microsoft SQL Server Express. Pick this one if your company is predominantly a Microsoft shop (or check with your colleagues to see what they already use)
• MySQL. This is a popular, widely used, database. There will be plenty of resources/tutorials online
• PostgreSQL. Another popular database - used by reddit. Again, you'll easily be able to find tutorials online.
• Oracle. A popular database, mainly used in the enterprise, by big companies. Pick this one if you are the kind of person that enjoys spending the weekend nailing your testicles to the floor.

As much as I hate to recommend w3schools, they do have a fairly good tutorial on SQL (the language used with databases). With your newly installed DB, you should learn...

• How to create a database
• How to create tables
• How to insert data into tables
• How to query data
• Indexes
• Foreign keys
• Joins - what are they, the different types etc.
• Updating data
• Deleting data

This would be enough to get you started. You'll have a good idea as to what to learn next once you've got to grips with the basics.

You might also want to check out /r/Database and /r/DatabaseHelp.