Basic relational database design is about logic and structure. When compared with other areas of computing, I would argue that the the original materials worked out by Codd and Date have not changed nearly as dramatically. There are certainly exceptional sub-areas where there have been major changes (e.g. the introduction of the object model and development of XML and RDF, to name but two prominent examples), but if I were you, I would suggest doing two things:
1. Do some research into existing relational database platforms (e.g. SQL Server, Oracle, PostGRES), figure out which model will ultimately work best for you, and get a book on that implementation of SQL and RDMS. Every intro to databases book has a chapter on relational database design. That will get you started. You can also skip the platform selection process if you are already stuck with a database.
2. Read this:
Date on Database: Writings 2000-2006 by C. J. Date
Codd (now deceased) and Date are still the authorities, IMHO, and this latter book will give you a good overview of major conceptual issues in relational database design.