umm.. let's see... here's a modified version with comments:

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

    my $dir = "c:/Xwords/";
    # my $n=length "c:/Xwords/"; # why do you need this?
    my $newDir = "c:/Xwords/PrintedXwords/";
    my @files;
    # you're better off doing this:

    opendir DIR, $dir or die "Cannot open directory: $!\n";
    @files = grep {/\.puz$/i} readdir (DIR);
    close DIR;

    foreach my $file (@files) {
         my $new = $file;
         my $from = $dir . $file;
         $new =~ s/\.puz$/A\.puz/;
         my $to = $newDir . $new;

         print " \n \n";
         print " full name of original file is $from \n";
         print " name of original file is $file \n";
         print " full name of new file is $to\n"; 
         print " \n \n";
    
        rename $from, $to;
     }


    print "Files renamed !";
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Update: fixed declarations.