DatabaseAnswers.org (unfortunately now defunct) but well-preserved in the Wayback Machine is a great source of example database schemas.
I can also recommend Beginning Database Design, published by Apress. I own this book and can confirm that it is of high quality. The book looks at a number of real world scenarios and explains the impact a certain design decision could have on the way the database works and the quality of the data and its output.
Finally I would advise building some small databases (E.G. contact management, Task list etc). Start by specifying some basic requirements and create some tables and queries. You WILL make some mistakes which is the best way of learning.