.htaccess

<IfModule mod_rewrite.c>
    RewriteEngine On
    RewriteCond %{REQUEST_FILENAME} !-d
    RewriteCond %{REQUEST_FILENAME} !-s
    RewriteRule ^(.*)$ rest/index.php?_rest=$1 [QSA,NC,L]
    RewriteCond %{REQUEST_FILENAME} -d
    RewriteRule ^(.*)$ rest/index.php [QSA,NC,L]
</IfModule>

Box.php

<?php
/**
 * Found at: Controllers/Box.php
 *
 * Handle requests to [URL]/Controllers/Box. Automagically handles CRUD (GET/POST/PUT/DELETE) for the xPDOObject class myBox.
 */
class myControllersBox extends modRestController {
    public $classKey = 'myBox';
    public $defaultSortField = 'name';
    public $defaultSortDirection = 'DESC';
}

index.php

<?php
/**
 * Place in /rest/ directory of site. Add .htaccess file above. Note that our REST controllers are in /rest/Controllers/; they can be anywhere though - just change the basePath config option.
 */

/* first load MODX externally */
require_once '/path/to/modx/config.core.php';
require_once MODX_CORE_PATH . 'model/modx/modx.class.php';
$modx = modX::getInstance('rest');
$modx->addPackage('myboxes','/path/to/myboxes/model');

/* now load the REST service */
$rest = $modx->getService('rest','rest.modRestService','',array(
    'basePath' => dirname(__FILE__).'/Controllers/',
    'controllerClassSeparator' => '',
    'controllerClassPrefix' => 'myControllers',
    'xmlRootNode' => 'response',
));
$rest->prepare();
if (!$rest->checkPermissions()) {
    $rest->sendUnauthorized(true);
}
$rest->process();

output-box.js

/**
 * A GET request to our controller at /rest/box.js will output something like this:
 */
{
   results: [{
      id: 1,
      name: 'A Blue Box',
      width: 20,
      height: 40
   },{
      /* etc */
   }]
   ,total: 23
}

output-box.xml

<!--
 A GET request to our controller at /rest/box.xml, however, will output something like this - the class automatically handles XML/JSON output types:
-->
<response>
  <results>
    <result>
      <id>1</id>
      <name>A Blue Box</name>
      <width>20</width>
      <height>40</height>
    </result>
    <result>
      <!-- etc -->
    </result>
  </results>
  <total>23</total>
</response>