You can take advantage of the WordPress.com Related Posts functionality to return related posts quickly. Enable it by turning on Related Posts in Settings > Reading and you’re done!
If you’d like to programmatically retrieve and display posts within your theme code, you can do so like this:
$posts = Jetpack_RelatedPosts::init_raw()->get_for_post_id( $post_id, $args ); // Returns an associative array in the form of id => $post_id: /* array( 'id' => 12345, 'id' => 54321 ) */
Note: This function performs an HTTP request to the REST API, so object caching should be added around the results.
Related Posts indexing will work regardless of whether your site is marked as “Private.” For self-hosted sites, Related Posts will currently only work for standard post-types; we are working on enabling it for custom post types.
For more information about ways to customize related posts, see http://jetpack.me/support/customize-related-posts/