There are modules for an insanely wide variety of tasks, so specific pointers are a bit hard to give. Like it was said before, start with the modules in the core distribution.

Reading the documentation about all the modules on CPAN is indeed a big task, but the division in categories and subcategories is a very useful feature. Browse the docs on a module you think is appropriate for the problem at hand, see what (if any) rating it has. Search PerlMonks for opinions that people have about that specific module. And, very important, use the module in some small script, just to test it out. Reading the docs is important, but getting a feel for its usefulness comes from actually using it.

Arjen