You can move your database through phpMyAdmin. You'll find the link for that at the bottom of the database managment page. Open it up and chose the database you want to move. You'll see a tab up on top that says "Export". Make sure you select all the tables and check off data and use complete inserts to be safe. Check off "Save as File" and then hit GO. You'll also see an option for compression and you may want to zipp or gzipp the database if its large. The only problem with this is that if its a large database, when you go to restore the database phpMyAdmin may timeout due to restrictions set on how long a PHP program can be run. If that happens don't be afraid of asking for help from your host.