The below filters can be added to a theme’s functions.php, but you have to make sure that your theme uses the post, body, and comment class functions, and that it doesn’t style hfeed or hentry. Also, hfeed is often added to the theme, and should be removed to avoid duplication.

/**
 * Adds custom classes to the array of body classes.
 *
 * @param array $classes Classes for the body element.
 * @return array
 */
function body_classes( $classes ) {
	// Adds a class of hfeed to non-singular pages.
	if ( ! is_singular() ) {
		$classes[] = 'hfeed';
		$classes[] = 'h-feed';
	} else {
		if ( 'page' !== get_post_type() ) {
				$classes[] = 'hentry';
				$classes[] = 'h-entry';
		}
	}
	return $classes;
}
add_filter( 'body_class', 'body_classes' );

/**
 * Adds custom classes to the array of post classes.
 *
 * @param array $classes Classes for the body element.
 * @return array
 */
function post_classes( $classes ) {
	$classes = array_diff( $classes, array( 'hentry' ) );
	if ( ! is_singular() ) {
		if ( 'page' !== get_post_type() ) {
			// Adds a class for microformats v2
			$classes[] = 'h-entry';
			// add hentry to the same tag as h-entry
			$classes[] = 'hentry';
		}
	}
	return $classes;
}

add_filter( 'post_class', 'post_classes' );

Now the below adds microformats 2 classes to the avatar photo and to comments.

/**
 * Adds mf2 to avatar
 *
 * @param array             $args Arguments passed to get_avatar_data(), after processing.
 * @param int|string|object $id_or_email A user ID, email address, or comment object
 * @return array $args
 */
	function get_avatar_data($args, $id_or_email) {
	if ( ! isset( $args['class'] ) ) {
		$args['class'] = array( 'u-photo' );
	 } else {
		$args['class'][] = 'u-photo';
	 }
	return $args;
	}

add_filter( 'get_avatar_data', 'get_avatar_data', 11, 2 );

/**
 * Adds custom classes to the array of comment classes.
 */
function comment_classes( $classes ) {
	$classes[] = 'u-comment';
	$classes[] = 'h-cite';
	return array_unique( $classes );
}

add_filter( 'comment_class', 'comment_classes', 11 );

This allows for the simplest conversion of themes to the basic Microformats 2 structure. In the second part, we start moving into other more invasive modifications of the theme.