A lot of tutorials online make it seem rather difficult to use different domains for different blogs in your WordPress multisite installation. Depending on your server configuration I’m sure there are potential issues but it can be really simple.
1. You need to have 2 or more domains pointed to the same location and this location must be a root folder installation of WordPress multisite.
2. Download and install WordPress MU Domain Mapping plugin. Follow the installation instructions on the plugin page.
3. In the WordPress administration for the blog you want to set a domain for go to Tools/Domain Mapping. Add your (new) domain name and select “Primary domain for this blog”. Save.
4. You’re done!
If you have any problems during the installation it might be because of how your host handles domains. Remember that all domains must point to the same root folder install of WordPress. If you get problems you can always ask at the support forum for WordPress MU Domain Mapping.