Google's auto completion gets added to the search field of the standard search block by default. So, you don't need to do anything if that is what you are looking for.
If you want to append auto completion to a different text input field, just add the css class "dm-autocompletion" to the element. All text input fields with the class "dm-autocompletion" will get Google's auto completion.
If you want to define your own css selectors which mark the auto completion input fields, add the site constant AUTO_COMPLETION_CSS_SELECTORS to the concrete5 config file config/site.php.
E.g., define('AUTO_COMPLETION_CSS_SELECTORS', '.my-class, #some-id');
For styling the auto completion drop box, modify the file packages/google_auto_completion/css/google_auto_completion.css.
Google Auto Completion supports multilingual sites. The auto completion values will be set to the language setting of the page. The add-on is checking if the Internationalization add-on is installed and if it can take the language from there. If this is not the case, it tries to read the localisation setup of concrete5. As last attempt it reads the localisation setup of the user's browser. If everything fails, the add-on assumes the page is in english.
Note: This add-on does not add Google Search. It adds Google's auto completion functionality.
If you need more control over your auto competion values, have a look at the Search Auto Completion add-on. It includes Google's auto completion plus features like creating your own stock of auto completion values and tracking your users' inputs.