IMHO the best way to learn is have a problem to solve. I first started using perl when a testing application was generating reams of logfiles, with the nuggets of useful info buried in the noise.
My first perl script simply took one type of logfile and gathered up the useful info and output it. I then combined the separate scripts for separate test types into one unified script that could read the logfile and figure out what to do.
This progressed to a script that could run on the command line or under Apache as a cgi and modify the output accordingly. At each step I learned a little more to do the next task.
One of the cool things about perl is you don't need to know very much to do something useful. As your needs grow, so does your knowledge. And even after doing it for 12 or so years, I keep my trusty camel book close at hand, because I can't remember every single function, or the order of the arguments of something I don't use very often.