This isn't the easiest project to learn Perl with, but it's a lot more exciting than making "Hello world!" programs. I myself learned Perl by making an online forum, complete with login and managing sessions through cookies. I'll give you a few pointers, and then if you have more questions, come back and post some specifics.
- Read Ovid's CGI course - the entire thing. If you find yourself getting impatient with reading, then take what you learned to go code some, and then come back to the CGI course later and read some more.
- Start small and code modular. Start with a plain text delimited file for usernames and passwords, and write a subroutine that verifies a user's credentials as input. This is a great way to get logins working, and allows for easy debugging (if you need to check that a password for a new account is getting stores correctly, it's plain text in the file). Once everything is working correctly, you can worry about upgrading your security to the point at which you feel comfortable.
Good luck, and have fun.