If you are on OS X, Transmit is a really nice FTP/SFTP application, but it costs money. Cyberduck is almost as nice and is free. Either one should let you drag and drop the bulk of your site onto the remote server. You'll obviously need to make sure mysql is setup on the remote server and you might need to edit the wp-config.php file (or whatever its called) to make sure paths and things are set up correctly for the remote server.

