As you loop through the input lines just set a flag where you need to. Then when you get to the next line do whatever you need to. You might also want a check at the end of the loop to see if your input didn't end properly.

#!/usr/bin/perl -w

use strict;

my $line;
my $pattern = "asdf";
my $flag = 0;

while($line = <>) {

    if($flag) {
        print "do something here to $line \n";
    }

    if($line =~ m/$pattern/) {
        $flag = 1;
    } else {
        $flag = 0;
    }
}

if($flag) {
    print "Oops, we don't have a line to work on but flag was set.\n";
}
[download]