I've always found it useful to use indentation to indicate program calling depth. While it is very simple, that makes it easy to keep straight how many call frames are open at any point, and what they are. (All the statements from a particular call to the function should line up nicely.)

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

my $recursion = 0;

sub hanoi {
   my ($n, $start, $end, $extra) = @_;
   $recursion++;
   my $indent = "  " x $recursion;

   print $indent, "Entering hanoi($n, $start, $end, $extra)\n";

   if ($n == 1) {
       print $indent, "Move disk #1 from $start to $end.\n";
   } else {
        hanoi($n-1, $start, $extra, $end);
        print $indent, "Move disk #$n from $start to $end.\n";
        hanoi($n-1, $extra, $end, $start);
   }
   print $indent, "Leaving hanoi($n, $start, $end, $extra)\n";
   $recursion--;
}

hanoi(3, 'A', 'C', 'B');
__END__
  Entering hanoi(3, A, C, B)
    Entering hanoi(2, A, B, C)
      Entering hanoi(1, A, C, B)
      Move disk #1 from A to C.
      Leaving hanoi(1, A, C, B)
    Move disk #2 from A to B.
      Entering hanoi(1, C, B, A)
      Move disk #1 from C to B.
      Leaving hanoi(1, C, B, A)
    Leaving hanoi(2, A, B, C)
  Move disk #3 from A to C.
    Entering hanoi(2, B, C, A)
      Entering hanoi(1, B, A, C)
      Move disk #1 from B to A.
      Leaving hanoi(1, B, A, C)
    Move disk #2 from B to C.
      Entering hanoi(1, A, C, B)
      Move disk #1 from A to C.
      Leaving hanoi(1, A, C, B)
    Leaving hanoi(2, B, C, A)
  Leaving hanoi(3, A, C, B)
[download]

As the saying goes, to understand recursion you must first understand recursion. But hopefully this simple output will help you get that "ah hah!" moment where it starts to make sense.

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