I don’t think you have to register jquery. I just put this in my functions.php:
function my_scripts_method() {
wp_enqueue_script(
'main',
get_template_directory_uri() . '/js/main.js',
array( 'jquery' )
);
}
add_action( 'wp_enqueue_scripts', 'my_scripts_method' );
It includes my custom scripts that are reliant on jquery.