Other approaches using a for-loop are perfectly OK and you should be sure you understand them. But as you gain more experience with Perl, you'll see that there's a good deal of wasted motion there. Here's a solution I find neat and easy to understand — once you understand the powerful map built-in!

c:\@Work\Perl\monks>perl -le
"use warnings;
 use strict;
 ;;
 use List::Util qw( min max );
 ;;
 my @not_normalized = qw(5 4 9 9 6);
 ;;
 my @normalized = normalizer(@not_normalized);
 ;;
 printf qq{$_  } for @normalized;
 ;;
 sub normalizer {
   my $min_numarray = min @_;
   my $max_numarray = max @_;
   my $numden = $max_numarray - $min_numarray;
   ;;
   return map { ($_ - $min_numarray) / $numden } @_;
   }
"
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The next thing to understand is that if you are processing a large array (and what is "large" depends on your circumstances), it may be advantageous to pass (and perhaps return) the array by reference; see perlref and perlreftut.

Update: And if you can stand to operate on the elements of the array in place (definitely fastest for large arrays), here's yet another approach:

c:\@Work\Perl\monks>perl -le
"use warnings;
 use strict;
 ;;
 use List::MoreUtils qw(minmax);
 ;;
 my @array = qw(5 4 9 9 6);
 ;;
 normalizer(@array);
 ;;
 printf qq{$_  } for @array;
 ;;
 sub normalizer {
   return unless @_ >= 2;
   my ($min, $max) = minmax @_;
   my $numden = $max - $min;
   ;;
   $_ = ($_ - $min) / $numden for @_;
   }
"
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This depends on the aliasing of the  @_ function argument array. See perlglossary for a brief discussion of the concept of an alias. Also see aliasing in Wikipedia.