I agree generally with
chromatic's answer,
although "just sitting down and programming"
could, I think, seem like a relatively daunting
task for someone who's never programmed at
all. :)
I came in to Perl already quite familiar with
C++, so from that perspective I already learned
a lot of the basics of programming; the sort of
concepts that can apply to any language. If you're
not familiar with those, I suspect it's a bit
more difficult to just sit down and learn a new
language *and* how to program, in general.
I think I'd recommend a beginning programmer's
book, such as Elements of Programming with Perl.
From there you can learn the basics, and once
you've learned those, I agree completely with
chromatic: learn new things by finding problems
you want to solve, and jump right into solving
them. Don't be afraid to look at other code (but
try to find good code, not code that hasn't been
touched since Perl 4 was in its heyday). One
source for good code, I think, is Randal
Schwartz's Web Techniques column. Practical, applied
uses of Perl. Start with the first few, then work
up to the later (more complicated) scripts. The
Unix Review columns are good too.