I have a copy of "Programming the Perl DBI" and its certainly still relevant. You don't say whether or not you have experience with SQL, but you will quickly need to tangle with it. I recommend "Learning SQL" by Alan Beaulieu. This book starts from ground zero and uses MySQL for the examples using the mySQL command tool.
Update: RE: moving from "flat files" to DB... The DBD-CSV module is a pretty good step to using SQL with the Perl DBI while accessing the CSV flat file format that we both love and hate. CSV is loved because of its seeming simplicity and hated because of the tricky details (like commas within quotes: "some text, that is one thing but has a comma"). Get the basics of SQL. That knowledge translates very directly into DBI syntax. But since the .CSV format is text, it is very easy to see what your DBI SQL statements actually did to the DB.
BTW,Some of the DB's that I use export their "CSV" data using the pipe "|" instead of a comma ",". Excel can understand that format. So "CSV", "Comma Separated Value" can use a different field separator than ",". Keep that in mind when generating CSV files.