Well, the first thing I'd want to do is allow all the input to come from a named file -- or if I choose to type, make it easier/quicker to enter values. Nothing strikes me as more tedious or error-prone than typing a bunch of values, one per line, in response to prompt strings while a program is running. So:

#!/usr/bin/perl -w
use strict;

my $Usage = <<ENDUSE;
Usage: $0 [punnett_square_specs.file]

 input data should contain two rows of values:
  first row lists pairs for the top of the punnett square
  second row lists pairs for the side of the punnett square

ENDUSE

die $Usage if(@ARGV and ! -r $ARGV[0]);

my @top = split /\s+/, <>;
my @side = split /\s+/, <>;

for my $t ( @top ) {
   for my $s ( @side ) {
      print "$t$s\n";
   }
}
[download]

I'm just taking it for granted that this really is the output format that you want (two values per line, number of lines = scalar @top * scalar @side). Prompting for $numtop and $numSide seems unnecessary -- just count up how many space-separated tokens are provided for each set.

As I've written it here, you can still type in the values after you start the program (or paste in lines of values from some other window); but you can also save your values in a file, and have it read that file, or you may have some other process that outputs the two lines of values, and pipe it to the script.

update: If, as suggested by BrowserUK's reply, you really want to print out something that looks like a square (i.e. a table) rather than just a list of lines (the way the OP code was written), then I'd change my loop to look like this (taking the terms "top" and "side" literally here):

print join( "    ", "  ", @top, $/);
for my $s ( @side ) {
    print "$s ";
    for my $t ( @top ) {
        print "  $t$s";
    }
    print $/;
}
[download]

Given two lines of input like:

gg hh kk jj
11 22 33 44
[download]

That loop will produce:

      gg    hh    kk    jj    
11   gg11  hh11  kk11  jj11
22   gg22  hh22  kk22  jj22
33   gg33  hh33  kk33  jj33
44   gg44  hh44  kk44  jj44
[download]