1: Grab all the files from your old host and upload to your new host.
2: take a backup of your old host database
3: Create a new empty database in your new host noting the name, user and password
4: Use the PHPmyadmin, open your new database and use the import function
5: select your downloaded database you took from the old host and press "go"
6: Now edit your config.php in /ow_includes/ and enter in your new site URL (if it has changed), the new username and password for your database connection.
That SHOULD be it. I have done this loads of times.