Add jQuery to WordPress page

I need to add jQuery library to WordPress page. The page is rendered by a plugin shortcode.

I've used the below methods but I don't see it working for my jQuery script.

I tried to add these below script in main plugin file where the plugin name and version go.

DESN'T WORK:

function my_init() {
    if (!is_admin()) {
        wp_enqueue_script('jquery');
    }
}
add_action('init', 'my_init');

DESN'T WORK

function my_init() {
    if (!is_admin()) {
        // comment out the next two lines to load the local copy of jQuery
        wp_deregister_script('jquery'); 
        wp_register_script('jquery', 'http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js', false, '1.4.2'); 
        wp_enqueue_script('jquery');
    }
}
add_action('init', 'my_init');

I actually need to add below library to my WordPress front end page?

http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js

but if i use it directly like below then it works.

<script type="text/javascript" src="//ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js"></script>

Second, How can see it loaded in my browser loaded along with other code?