Download the database from your existing host. Upload vBulletin to your new host, install it, then upload the database to replace the one you set up with the new installation.
Don't forget, you have to update your index.php with the new server info! Check it twice as this is usually the case of why things don't work after a move!
Its quite simple, just copy all the files and the database. If you need help feel free to add me on msn Or if you want me to move it for you I can do it for $3.