Are you switching hosting accounts, etc too, or is it really just a new domain name?
Hosting does not change, same host account, same mysql database, etc. Only changing domain name:
Point the domain to the IP of the server, change the virtual host to the new domain.
Go to xenforo's admin > board options > and change to the new url.
If you are changing host as well as domain, so it's about the xenforo files and the database, then :
-Go to xenforo's admin > board options > and change to the new url.
- export the xenforo directory, and any other file that you need for your site to a zip file (or .tar.gz)
- export the xenforo mysql database, and any other database that you need for your site to a zip file (.sql.gz)
go to the new host, put the files there, and unzip it. import the database into a new database, and go to library/config.php and point it to the new database. Point the domain to the IP, set up a virtual host for the domain and load up the site.