Use xcart administration DB backup.
Remove most of the files inside /xcart/var except the /cache folder and the /tmp folder with the sql backup.
Tar the xcart folder
tar cvfp xcart.tar xcart
FTP these files to the new server and untar them.
tar xvfp xcart.tar
modify the xcart/config.php
Go into /phpmyadmin and add the database and user
Import the database
mysql -u root -ppassword database < dump.sql (insert the correct info here)
Check if there are other tables that aren't xcart. Export them from the old database and import them into the new database using phpmyadmin.
Check the public pages and administrator pages in the browser.