It depends on how you use Perl to do your HTTP requests.
Given you would like to use LWP, you find an example in it's manual when you go looking for "POST".
...actually, you still have to do a little guessing and tinkering, but it will give you the idea.

If you want to use CGI.pm, you could use the post method in the form. However, you need the user to click the submit button then, you cannot do it by HTTP redirect which only works as a GET.

Cheers, Sören