Here are the steps involved when moving a WordPress Multisite installation to a new domain name. In my case I wanted to move everything (code + database) from development to production.

After copying everything to the new environment, you have to change the following items:

Make sure to add or update your wp-config.php file:

define('DOMAIN_CURRENT_SITE', 'mynewdomain.com');
define('PATH_CURRENT_SITE', '/');

And in your database update the following tables and fields:

• Update the domain and path fields in the wp_blogs and wp_site table
• Update the value of the field with siteurl key in the wp_sitemeta table
• Update the values of the fields with siteurl and home key in the wp_options table and every other wp_[BLOGID]_options table