I think that doing the exercises in Learning Perl is a very good way to start. If you don't have the book, get it; if you already have it, give it another chance.

It was easy for me to learn Perl because I started using it from day 1 at work. (It helped that my OS was some Unix flavor or other, so Perl fit right in.) I wrote hundreds of short (10-50 line) scripts, mostly for munging text files and analyzing their contents. First I wrote these scripts for my work, but then cow-orkers who were amazed at the magical powers of Perl (and too lazy to learn it themselves) started asking me to write scripts for them.

So I would recommend starting small with simple munging scripts, and work your way up to full-blown applications. The project that you're setting yourself to do seems to me a bit ambitious, unless you have a lot of non-Perl programming experience in that area already. If the latter is the case, you may be able to get something to work using recipes from The Perl Cookbook, but sooner or later you will have to buckle down and learn the basics.