The technique is to use recursion. Maybe it is clearer if we get the code to actually move the "rings" and show the state of the piles after each move? Consider:

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

my %piles = (A => [reverse 1..3], B => [], C => []);

dumpPiles ();
hanoi (scalar @{$piles{A}}, keys %piles);

sub hanoi {
   my ($n, $start, $end, $extra) = @_;
   if ($n == 1) {
        report ($start, $end);
   } else {
        hanoi($n-1, $start, $extra, $end);
        report ($start, $end);
        hanoi($n-1, $extra, $end, $start);
   }
}

sub report {
    my ($start, $end) = @_;
    my $disk = pop @{$piles{$start}};

    print "Moved disk $disk from $start to $end.\n";
    push @{$piles{$end}}, $disk;
    dumpPiles ();
}

sub dumpPiles {
    for my $pile (sort keys %piles) {
        print "$pile: @{$piles{$pile}}\n";
    }
}
[download]

Prints:

A: 3 2 1
B: 
C: 
Moved disk 1 from A to C.
A: 3 2
B: 
C: 1
Moved disk 2 from A to B.
A: 3
B: 2
C: 1
Moved disk 1 from C to B.
A: 3
B: 2 1
C: 
Moved disk 3 from A to C.
A: 
B: 2 1
C: 3
Moved disk 1 from B to A.
A: 1
B: 2
C: 3
Moved disk 2 from B to C.
A: 1
B: 
C: 3 2
Moved disk 1 from A to C.
A: 
B: 
C: 3 2 1
[download]