Ok well its 8:30 here and i need to get out to work, im about later on and can help if you still need me.
Basically just download all your files and then upload to the new server, then do a database dump of your existing db, import that to your new mysql db and then edit the local.config.php file with your new connection information.
You will need to update the dns to your new server which can take up to 24 hours but is usually quicker than that, the only other thing to watch is your directory permissions, just make sure the correct directories have the correct permissions.