Ultimately the answer, in some form or another, is threads. The tutorials section contains Threads: why locking is required when using shared variables and Things you need to know before programming Perl ithreads, neither of which is a tutorial that introduces the concepts you require, nor paints in the big yellow and black warning borders around the tricky areas. The Perl documentation contains perlthrtut, which may be a good start. Another way to go about things (by hiding the tread stuff under the hood somewhat) is to use POE.

Beware, threads can be tricky creatures that bite in nasty and unusual ways. On the other hand, there are a few Perl Monks around with a fair amount of experience taming them so pleas for help will certinally be answered. Good luck ;).