<section id="left">
      <label for="form_name">Name</label>
      <input name="form_name" id="form_name" type="text" >

      <label for="form_email">Email</label>
      <input name="form_email" id="form_email" type="email" >
   </section>

   <section id="right">
      <label for="form_msg">Message</label>
      <textarea name="form_msg" id="form_msg"></textarea>
      <input id="submit" class="button" name="submit" type="submit" value="Send">
   </section>

</form>

$(function() {
    $("#contact .button").click(function() {
        var name = $("#form_name").val();
        var email = $("#form_email").val();
        var text = $("#msg_text").val();
        var dataString = 'name='+ name + '&email=' + email + '&text=' + text;

        $.ajax({
            type: "POST",
            url: "email.php",
            data: dataString,
            success: function(){
            $('.success').fadeIn(1000);
            }
        });

        return false;
    });
});

<?php
if($_POST){
    $name = $_POST['form_name'];
    $email = $_POST['form_email'];
    $message = $_POST['form_msg'];

//send email
    mail("email@gmail.com", "This is an email from:" .$email, $message);
}
?>

var data = {
    name: $("#form_name").val(),
    email: $("#form_email").val(),
    message: $("#msg_text").val()
};
$.ajax({
    type: "POST",
    url: "email.php",
    data: data,
    success: function(){
        $('.success').fadeIn(1000);
    }
});

var name = $("#form_name").val();
        var email = $("#form_email").val();
        var text = $("#msg_text").val();
        var dataString = 'name='+ name + '&email=' + email + '&text=' + text;

        $.ajax({
            type: "POST",
            url: "email.php",
            data: dataString,
            success: function(){
            $('.success').fadeIn(1000);
            }
        });

$.ajax({
        type: "POST",
        url: "email.php",
        data: $(form).serialize(),
        success: function(){
        $('.success').fadeIn(1000);
        }
    });

var dataString = 'name='+ name + '&email=' + email + '&text=' + text;
                      ^^^^-$_POST['name']
                                       ^^^^--$_POST['name']
                                      etc....

if($_POST){
    $name = $_POST['name'];
    $email = $_POST['email'];
    $message = $_POST['text'];

//send email
    mail("j.andrew.sears@gmail.com", "51 Deep comment from" .$email, $message);
}

<?php
if($_POST){
    $name = $_POST['name'];
    $email = $_POST['email'];
    $message = $_POST['text'];

//send email
    mail("j.andrew.sears@gmail.com", "51 Deep comment from" .$email, $message);
}
?>

<section id="right">
      <label for="form_msg">Message</label>
      <textarea name="form_msg" id="#msg_text"></textarea>
      <input id="submit" class="button" name="submit" type="submit" value="Send">
   </section>

var data = {
    name: $("#form_name").val(),
    email: $("#form_email").val(),
    message: $("#msg_text").val()
};
$.ajax({
    type: "POST",
    url: "email.php",
    data: data,
    success: function(){
        $('.success').fadeIn(1000);
    }
});

<?php
if($_POST){
    $name = $_POST['name'];
    $email = $_POST['email'];
    $message = $_POST['text'];

//send email
    mail("email@gmail.com", "My Subject:",$email,$message);
}
?>