Untested code using Mail::Sendmail to give you an idea why using a module is far better :)

#!/usr/bin/perl -wT

use strict;
use CGI;
use Mail::Sendmail;

my $q = new CGI;

my $name    = $q->param("name");
my $email   = $q->param("email");
my $message = $q->param("message");

# Config

my $adminmail = "admin\@yoursite.com";
my $from      = "whoever\@whatever.com";
my $subject   = "enter subject here";

# End config

my %mail = ( To      => "$adminmail",
             From    => "$from",
             Subject => "$subject",
             Message => "$message" );

sendmail(%mail) or die $Mail::Sendmail::error;

print $q->redirect("thanks.html") or die "Can't find thanks.html: $!\n
+";
[download]

Update: You should include Juerd's improvements listed below.

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