These are from the manual:
Backing Up The Database via SSH/Telnet or
Backing Up The Database via phpMyAdmin
Restoring The Database via SSH/Telnet or
Restoring The Database via phpMyAdmin
If you don't have shell access, some people have also reported success with these scripts:
MySQLDumper
MySQLHotxcopy
Bigdump
You may want to head over to vbulletin.com because the whole installation process has been discussed several times before (I think there is even an article on it).