You have been bitten by omitting use strict;use warnings. Specifically, on line 8 you say "scalar @{$hash_ref{$key}}" which is trying to access a non-existent hash named %hash_ref instead of a scalar named $hash_ref. You require the dereference operator to get that result; see perlreftut. You do the same on line 9.

Adding strictures and fixing that mistake gives:

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

my $hash_ref = set_up();

foreach my $key (keys %{$hash_ref}) {
   my $val = $$hash_ref{$key};
   if (ref($val)) {
      print "\ntotal \'$key\' = ", scalar @{$hash_ref->{$key}}, "\n";
      foreach my $act (@{$hash_ref->{$key}}) {
         print "\t$act\n";
      }
   } else {
      print "$key - $val\n";
   }
}

sub set_up {

   my (%hash,@array);

   @array=("feed","walk","pet","groom");
   $hash{'one'}="cat";
   $hash{'two'}="dog";
   push(@{$hash{'actions'}},@array);

   return(\%hash);
}
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