What you see in the screenshot is the screen of a Custom Post Type. In the documentation you will find an example code on how to add such a screen.
About where to place the code - it depends. Do you want to be able to use this Custom Post Type in other themes, or you will only need it in this theme?
If you want to use it in other themes as well, put the code in your plugin's code.
If you want to use it only in this theme, put it in your theme's functions.php.
And in case you still want to add a custom menu page, here you will find examples on what is the proper way to use this function. What you should note, is that the call to add_menu_page() should be done inside a function that is run on the admin_menu action.
Here's an example working code with WP 3.4.2
function register_custom_menu_page() {
add_menu_page('custom menu title', 'custom menu', 'add_users', 'custompage', '_custom_menu_page', null, 6);
}
add_action('admin_menu', 'register_custom_menu_page');
function _custom_menu_page(){
echo "Admin Page Test";
}