this is a complex task (and takes even longer if you have many subsites already).
THINGS TO THINK ABOUT
Basically allow yourself 48 hours and start by making a list of all things that will be affected such as:
- Google Webmaster Tools
- Google Analytics
- Twitter / Facebook & losing all the social sharing stats
- How many domains to change
- DNS settings / cpanel settings
- 301 redirect everything
How many Subsites do you have?
You will need to make database table changes for every subsite ... manually ...
you need to change wp_siteid_options for each site
Don't rely on search and replace for oldsite.com -> newsite.com
First reason is that your web host may have directory structure like
So any linked images or files will break if you just do a search & replace.
WordPress Multisite has this table you'll need to check and make changes to it.
You'll need to setup a 301 redirect for oldsite.com -> newsite.com
See also http://wordpress.damien.co/2012/05/change-your-wordpress-multi-site-domain-url/