Ok, I have time.
My first set of instructions show you how to use SSH to backup a database. This avoids having to do it through a web based phpmyadmin panel or somesuch.
So if you follow the first instructions you should have an sql backup file in your directory.
Now we are going to skip transferring it to your computer and then uploading it to the new server.
We will do this by transferring the file directly from one server to another using the wget command.
I am again making assumptions about what your new box is running.
A) log into your new server through SSH
B) type the following ccommand:
C) move the backup file to your new virtual directory with the mv command
mv ~/backup.sql /home/tom/backup.sql
of course make sure to get the directories right.
D) now you need to restore the database through SSH.
use the following command (remember to use your username and other such details):
mysql $databasename -u $user -p$password < /home/$user/backup.sql
This should take a while, depending on your database size.
But afterward you should be all done.
I will write up some tutorials about this in the future.