Simply open you functions.php file (either in the dashboard or in your theme folder located in the file manager of your hosting account) and paste the following code at the bottom. You can also use a plugin called Code Snippets to add this code.
|// Remove Top Header Search Function|
|remove_action( 'genesis_header', 'essence_header_left_widget', 9 );|
If you are using a caching plugin or have caching enabled on your hosting account, you may need to clear the cache before you can see your changes.
If you would like to me to assist you with adding this to your website, contact me here.