Beginner trying to use jQuery in a custom location, but not sure where to insert the code
If you are customising a theme, I would add a custom jquery script you have written. In your themes template.php you can then simply call the .js file from within the theme folder.

For example you could add this to your template.php file:

drupal_add_js(drupal_get_path('theme', 'YOUR_THEME_NAME') . '/js/jquery.custom.js');


in the jquery.custom.js file you could have something like this:

(function($) {

 $(document).ready(function() {

  // hover effect
  $(".hover_effect").hover(function() { 
    //add effects here 
  }

 }); 

}(jQuery));