How to send data to the server via Ajax?

This is all greatly simplified but on the javascript side, you could do this:

var params = {"email": $("input#email")
$.post(yourserver.php, params, validate, "json")

function validate(response) {

  if (response.success) {
    console.log("Allgood")
  } else {
    console.log(response.message)
  }

}

and on the php server side, your server.php could look like this:

<?
  if ( $_REQUEST["email"] ) {
    $response = array("success" => true)
  } else {
    $response = array("success" => false, "message" => "Missing email");
  }

  echo json_encode($response);
?>