how to connect the author profile with google webmaster tools in multiuser blog?

Author info is two steps:

  1. Link pages on your site to the Author’s Google+ Profile, the easiest way being a rel=”author” <link /> tag in the <head> section.
  2. Authors link the the site on their Google+ profile, the “contributes to” section (or whatever that happens to be called.

Step 1 has to do with WordPress. Step 2 is up to the author. A blog that has multiple authors is no different from one that has one. You just need to output the rel=”author” tag on a per author basis. Which means you need to add a field to each user’s page where they (or the site admin) can input a Google+ link.

Fortunatley this is really easy: hook into user_contactmethods to insert a new field into the contact methods area of the user form for Google+, then use the value there to output a rel=”author” tag in the head section. Because it’s per user (author) each individual post will have it’s own rel=”author” tags.

The example below is limited to singular pages (posts, pages, custom post types), but you could easily expand it.

<?php
add_filter('user_contactmethods', 'wpse83193_user_contactmethods');
/**
 * Adds a Google+ field to the contact methods area in the user's profile.
 *
 * @param   array $contact key => label pairs of contact methods
 * @return  array Same as the input: key => label pairs
 */
function wpse83193_user_contactmethods($contact)
{
    $contact['wpse83193_google'] = __('Google+', 'wpse');
    return $contact;
}

add_action('wp_head', 'wpse83193_output_contactmethods');
/**
 * Spit out the rel=author link tag in the <head> section.
 *
 * @uses    is_singular
 * @uses    get_user_meta
 * @return  void
 */
function wpse83193_output_contactmethods()
{
    if (!is_singular()) {
        return;
    }

    if ($rel = get_user_meta(get_queried_object()->post_author, 'wpse83193_google', true)) {
        printf('<link rel="author" href="https://wordpress.stackexchange.com/questions/83193/%s" />', esc_url($rel));
    }
}

The above as a plugin.

There are also plenty of SEO plugins that do exactly what I showed above already built and ready to go.