there are lot of issue in your Module>Please check


My config file in `app/etc/module/dixit_featured.xml`
Path should be `Dixit_Featured.xml`  from  

    dixit_featured.xml
and code 

    <?xml version="1.0"?>
     <config>
      <modules>
         <Dixit_Featured> <!--  Dixit_Featured to  dixit_featured -->
    	<active>true</active>
    	<codepool>local</codepool>
          </Dixit_Featured> <!--  Dixit_Featured to  dixit_featured -->
      </modules>
     </config>

Created `Controllrer` in `app\code\local\dixit\featured\controllers\IndexController.php`
Path should be `app\code\local\Dixit\Featured\controllers\IndexController.`php


    <?php
    class Dixit_Featured_IndexController extends Mage_Core_Controller_Front_Action
    {
       public function indexAction ()
       {
        echo 'test index';
       }
       public function mamethodeAction ()
       {
        echo 'test mymethod';
        }
    }
    ?>

Class Should be  `dixit_featured_IndexController` from  `Dixit_Featured_IndexController`

And Created My Plugin xml file in `app\code\local\dixit\featured\etc\config.xml`
to 
change   xml file in `app\code\local\Dixit\Featured\etc\config.xml` and look like


    <?xml version="1.0"?>
     <config>
        <modules>
           <dixit_featured><!--  Dixit_Featured to  dixit_featured -->
    	  <version>1.0.1</version>
           </dixit_featured> <!--  Dixit_Featured to  dixit_featured -->
         </modules>
    <frontend>
    <routers>
         <mymodule>
    	<use>standard</use>
    	<args>
    	    <module>Dixit_Featured</module> <!--  Dixit_Featured to  dixit_featured -->
    	    <frontname>dixit</frontname>
    	</args>
         <mymodule>
    </routers>
    </frontend>
    </config>



Please study basic study of [module][1]


  [1]: http://www.amitbera.com/create-an-magento-extension-with-custom-database-table/