I presume you have already found the Tutorials section here. Once you are beyond the stage of simply closing your eyes or hurriedly looking away at the sight of a chunk of Perl script I strongly recommend that you look at the questions and answers in the Seekers of Perl Wisdom section here. That will give you a wide exposure to applications of Perl from the very mundane to the highly esoteric - just pick the questions you feel somewhat comfortable with or that seem applicable to your area of interest and then squeeze all the juice out that you can get.

Using Seekers of Perl Wisdom as a learning resource is a really good way of finding out about a lot of tricks, traps and generally cool stuff as well as getting a good feel for how to write practical Perl well.