This is super easy to do. Get a PHP mailer script. Create a form on your web site using HTML then have the form submit <form method="post" action="?"> I put action ? because it came back to my same page... however you can put it to another PHP file called something like mailsubmission.php... in that PHP file you need to get the variables from the form you submitted. Then you need to receive the form items into / from a Post Variable like this
$to = $_POST['to'];
$oldmessage = $_POST['message'];
$email = $_POST['email'];
$name = $_POST['name'];
$sent = $_POST['sent'];
Then use a PHP mailer script to then take those and mail them to the person you want to receive them. Plenty of tutorials on stack exchange how to further do that.
You can also harden the form itself making sure the expressions are legit with javascript if you want to verify things and make sure no one is hacking your form. Hope this helps.