Execute Jquery when a specific page in my plugin is loading

You’ll need to get the screen id on the screen (or page) in question using get_current_screen()

get_current_screen()->id

Then, hook into it with the following:

function my_script_function() {
    if ( strpos( get_current_screen()->id, 'screen_id' ) !== false ) {
        wp_enqueue_script( 'my_javascript_handle', 'path/to/my/script.js', 'jquery', '1.0' );
    }
}
add_action( 'admin_enqueue_scripts', 'my_script_function' );

This will enqueue your script properly in the WordPress system along with jQuery core (just in case it isn’t already there).

http://digwp.com/2009/06/including-jquery-in-wordpress-the-right-way/ has a good overview of using jQuery in WordPress. Please note that by default though you can’t use $ to call jQuery as it is in safe mode (the article will show you how to change it from having to use jQuery.