Is Perl the first programming language you are trying to learn? If so, and if you have not had any "formal instruction" in programming (i.e. a classroom environment), you might find it worthwhile to look for a programming class you can go to, even if it's not a class about Perl: having a teacher and fellow students to talk with about any programming language will be helpful, and you will be able to use what you learn in class when you work in Perl.

Since you have already been over the "Learning Perl" book, the next thing I would suggest is: find a perl program (for example a command-line tool) that does some task that you are interested in (for example moving data to or from a database or extracting content from HTML). Try it out, see what it does, and figure out how it does that.

Then think of some related thing that it doesn't do, but would be useful (for instance, reporting summary statistics when it's done), and modify it so that it does this new thing (either in addition to, or instead of, what it already does).

For every programming language I have ever used effectively, it is the case that I really started to learn it by working with someone else's code, changing a usable tool to do something new that I wanted. This has worked for me many times, and I recommend it.