I am running wordpress-mu using domains (site.mydomain.com). I have one particular site (onesite.mydomain.com) which also has its own domain name (i.e. otherdomain.net shows the same content as onesite.mydomain.com). Right now I'm using frame-based URL forwarding so that the user sees "otherdomain.net" in the address bar, but wordpress sees "onesite.mydomain.com" and serves the proper site.
Is there a better way to accomplish this that doesn't involve frames?
I'm not sure about for Wordpress-Mu, but for regular Wordpress, you would just serve otherdomain.net off the same machine that serves onesite.mydomain.com.
If you're using Apache, you would set modify the VirtualHost block to include a ServerAlias to otherdomain.net (assuming it's currently configured to onesite.mydomain.com). The Wordpress PHP will be hit to serve pages requested at either name.
I suppose Wordpress-Mu adds an additional layer of name resolution in order to pick which W-Mu site to serve. My guess is it has an alias mechanism as well, but if not then you might consider going from a Wordpress-Mu setup to a simpler standard Wordpress setup. You'll get fresher code and avoid Mu complications.
Actually, what you're looking for is the domain mapping plugin.
http://wordpress.org/extend/plugins/wordpress-mu-domain-mapping/