How to add a custom feed to WordPress

class-custom-feed.php

<?php
/**
 * Add a custom feed to WordPress.
 *
 * The feed will be rendered through the wp-includes/feed-rss2.php template
 * and avaiable under example.com/feed/{$feed_slug}.
 *
 * Note: Don't forget to flush the rewrite rules once.
 *
 * @author Dominik Schilling
 * @link   http://wpgrafie.de/897
 */
class DS_Custom_Feed {
	/**
	 * Sets the feed slug.
	 *
	 * @var string
	 */
	public static $feed_slug = 'custom';

	/**
	 * Registers the feed and the pre_get_posts action
	 */
	public static function init() {
		add_feed( self::$feed_slug, array( __CLASS__, 'feed_template' ) );

		add_action( 'pre_get_posts', array( __CLASS__, 'feed_content' ) );
	}

	/**
	 * Customizes the query.
	 * It will bail if $query is not an object, filters are suppressed and it's not
	 * our feed query.
	 *
	 * @param  WP_Query $query The current query
	 */
	public static function feed_content( $query ) {
		// Bail if $query is not an object or of incorrect class
		if ( ! $query instanceof WP_Query )
			return;

		// Bail if filters are suppressed on this query
		if ( $query->get( 'suppress_filters' ) )
			return;

		// Bail if it's not our feed
		if ( ! $query->is_feed( self::$feed_slug ) )
			return;

		// Change the feed content
		// Example: A feed for pages
		$query->set( 'post_type', array( 'page' ) );
	}

	/**
	 * Loads the feed template which is placed in wp-includes/feed-rss2.php.
	 */
	public static function feed_template() {
		load_template( ABSPATH . WPINC . '/feed-rss2.php' );
	}
}

/**
 * Hooks into `init`.
 *
 * Note: add_feed() needs access to the global $wp_rewrite
 */
add_action( 'init', array( 'DS_Custom_Feed', 'init' ) );