Here you go.

add_action(\'init\', \'register_custom_jquery\');
function register_custom_jquery() {
    wp_deregister_script(\'jquery\');
    wp_register_script(
        \'jquery\', 
        \'https://ajax.googleapis.com/ajax/libs/jquery/1.6.1/jquery.min.js\', 
        array(), 
        \'1.6.1\'
    );

    wp_register_script(
        \'my-custom-script\', 
        \'http://example.com/js/script.js\', 
        array(), 
        \'1.0\'
    );
}

add_action(\'wp_enqueue_scripts\', \'add_js_to_page\');
function add_js_to_page() {
    wp_enqueue_script( \'jquery\' );

    wp_enqueue_script( \'my-custom-script\' );
}