Copy the files and the DB to your new domain, then search for ALL instances of Oldomain.
HOWEVER. Do not do a blind replace. You don’t want to replace anything in widgets, but you DO want to replace wp_blogs, wp_sites, wp_posts and SOME wp_options.
WordPress uses a feature called serialization. That means that some of your data is stored with the LENGTH of the domain name. If you do a blind replace, you’ll lose your widgets and possibly screw up your media table, making everything invisible. Just don’t. Trust me on that one ??