|There's more than one way to do things|
If we take a step back and ask: "How do you learn anything worthwhile?" For ME it would be to start by surrounding yourself with everything having to do with the subject. In the case of Perl it's fortunate that there are lots of ways to do that.
I started learning Perl by surrounding myself with it as much as possible. I bought the recommended books in both paper and digital format. I have the Perl Cookbook on the home screen of my phone. My laptop's desktop background is the face of a camel (no — seriously >> It's a portrait of a camel). I shadow good Perl programmers by coming here to the Monastery and reading the blogs of well know people in the community. I've gone to a Perl user's meeting through Meetup.com (Check out if there's a local Perl Monger's group near you.) When I go out there's a Perl book in my hand with a notebook. I keep the radio off in my car to give me space to think about projects (Perl and otherwise). Like I said: Surrounded — Completely :-))
If you want to learn anything that's worth learning (like Perl, the guitar, math or how to draw etc.) they take a significant amount of your life to learn well (let alone to master). According to Malcolm Gladwell in Outliers, the 'magic number' is 10,000 hours. So patience would be my biggest recommendation. ;-)
As for books, if you're new to programming and the UNIX environment I would highly recommend Elements of Programming with Perl. If you're more advanced than that, I would agree with the previous mentions of Learning Perl and/or Perl Cookbook.
Good luck and have fun learning Perl!
"...the adversities born of well-placed thoughts should be considered mercies rather than misfortunes." — Don Quixote