You have a couple mistakes.

• my($#ARGV) = @_; makes no sense.

• $arg contains a number, so it'll never be equal to any of the strings to which you compare it. You would need to loop over @ARGV.

I'd use Getopt::Long.

use Getopt::Long qw( GetOptions );

sub usage {
   print STDERR "...simple usage...\n";
   exit(1);
}

sub help {
   print "...more extensive help...\n";
   exit(0);
}

GetOptions(
   'h|?|help' => \&help,
   ...
)
   or usage();
[download]

You might also find Pod::Usage of interest.