Hi Steve,
You can do a backup on your database, then copy the entire directory your site is on, (make sure you get all your files & images) then on your new server, Install a new version of MOS, then take your old files & install them right over the old ones, when prompted choose "overwrite all", Almost done

Now take the database backup & restore it VIA your admin panel.
Note.. You may need to correct some info (paths) in your config file.
Also..DO NOT delete anything from your old host untill your up & running with the new host.
That should do it..
Hope this helps
