How can I output the content of the page using this code?

This is a “custom” loop outside of the main WordPress query (query_posts), you will have to tell WordPress to setup the post data using setup_postdata()

More info on get_posts() is found here, giving you basically what I am about to write below: http://codex.wordpress.org/Template_Tags/get_posts

Tip: The WordPress Codex is the best friend you will ever have, apart from Google.

<?php

$the_slug = 'my-page';

$args = array(
    'name'          => $the_slug,
    'post_type'     => 'page',
    'post_status'   => 'publish',
    'numberposts'   => 1
);

$my_posts = get_posts($args);

if( $my_posts ) {

    echo 'ID on the first post found '.$my_posts[0]->ID;

    // To get the content of the first post:
    echo apply_filters('the_content', $my_posts[0]->post_content);

    // if you now wanted to remove the first post from this loop and assign it to a different variable $first_post
    // However, it looks as if you are only grabbing one "post" being a "page" from the slug "my-page"
    $first_post = $my_posts[0];
    unset($my_posts[0]);

    foreach($my_posts as $p): setup_postdata($p); 

        // Now you can use the_title(), the_content() etc as you normally would

    endforeach;

}

// Reset WordPress Loop & WP_Query
wp_reset_postdata();

?>

Related Posts: