I would have written the above logic like this

#!/usr/local/bin/perl
use strict;
use warnings;

my $input;
my $hrate = 0;
my $yrate = 0;

while (!defined $input) {
    print "\nDo you wish to calculate yearly salary (y) or hourly rate
+ (h)?";
    chomp ($input = <STDIN>);
    if ($input =~ /h/i) {
        print "\nEnter your yearly salary:";
        chomp ($yrate = <STDIN>);
        $hrate = ($yrate / 52) / 40;
        print "\nYour hourly rate is $hrate";
    }elsif ($input =~ /y/i) {
        print "\nEnter your hourly rate:";
        chomp ($hrate = <STDIN>);
        $yrate = ($hrate * 40) * 52;
        print "\nYour yearly salary is $yrate";
    }elsif ($input =~ /q/i) {
      exit;
    }else {
        print "\nError in input";
    }
    undef $input;  #to continue  in the loop
}
[download]

I would like to suggest that a good place to start learning Perl is to read "Learning Perl", published by O'Reilly & Associates. And one more book is freely available online. Name is Simon Cozens' Beginning Perl.