Invoking Jquery in a Plugin

To load default wordpess jquery you can use this

add_action( 'wp_enqueue_scripts', 'my_jquery' );

function my_jquery(){
  wp_enqueue_script("jquery");
}

And use jquery no conflict wrapper to avoid error or on your jquery code

(function($) {
    // Inside of this function, $() will work as an alias for jQuery()
    // and other libraries also using $ will not be accessible under this shortcut
})(jQuery);

Get more details on wp enqueue script