WordPress uses jquery by default and you dont have you do anything extra, most jquery scripts and plugins should pretty much work well by default. so, how to add jquery the correct way? Its easy and can be done with just 3 lines of code and can be done in a couple of ways.Go to functions.php of your theme and add this hook. Remember all functions according to wordpress standards, must be wrapped through a hook and all scripts and styles must be added through wp_enqueue_script() function.

To add your own js file, create a js folder under your theme directory and name the file as myscript.js.

function mytheme_jquery_setup() {
wp_enqueue_script('jquery');
wp_enqueue_script('myscript',get_template_directory_uri().'/js/myscript.js');
}
add_action ('wp_enqueue_scripts','mytheme_jquery_setup');

Thats it! jquery should work, the second way is, if you want to custom add the jquery urls like from google api, do this way

wp_enqueue_script('jquery','//ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js')