I would suggest using strict and warnings and setting values to empty string to avoid warnings. Try something like this:

#!/usr/local/bin/perl
use warnings;
use strict;
use CGI; 
my $script_URL = "url of script goes here";
my $query = new CGI;
print $query->header();
my $name = $query->param("f_name") || '';
my $tel = $query->param("f_tel") || '';
my $zip = $query->param("f_zip") || '';
if ( "$name$tel$zip" eq '' ) {  &showform;  }
else {
    print "Name: $name\n";
    print "Tel: $tel\n";
    print "Zip: $zip\n";
}
sub showform {
    print "<FORM ACTION=$script_URL METHOD=POST>\n";
    print "Name: <INPUT TYPE=text NAME=f_name SIZE=24 value=\"$name\">
+\n";
    print "Tel: <INPUT TYPE=text NAME=f_tel SIZE=12 value=\"$tel\">\n"
+;
    print "Zip: <INPUT TYPE=text NAME=f_zip SIZE=5 value=\"$zip\">\n";
    print "<INPUT TYPE=submit VALUE=\"SUBMIT\">\n";
}
[download]

update: added missing content-header