How to return data from PHP to a jQuery ajax call

I am posting some data using ajax. I want to manipulate that data and return to to the calling jQuery script.

Here is my jQuery:

$.ajax({
  type: "POST",
  url: "somescript.php",
  datatype: "html",
  data: dataString,
  success: function() {
    //do something;
    }
});

Here is my somescript.php on the server:

  <?php
    //manipulate data
    $output = some_function(); //function outputs a comma-separated string
    return $output;
  ?>

Am I doing this correctly on the server side, and how do I access the return string when the ajax call completes?