You need the following:

• DBI - The DataBase Interface module.
• DBD::mysql - The Database Driver for MySQL.
• Class::DBI (optional) - Database abstraction.

And while we're at it, I'll recommend "Programming the Perl DBI" (An O'Reilly & Assoc. book). I found it quite helpful. If you need to learn SQL too, there are a million books out there on that subject.

All three of those modules are available on CPAN, as well as via PPM for Windows users.