There’s not going to be any way to insert and be done with it, but possibly you could try just hooking WordPress’s search function to the theme’s action present there to get you started. This would go in your Child theme’s functions.php, for example.
add_action( 'themeblvd_header_menu_addon', 'get_search_form' );
From there, you’d need to make CSS customizations I’m sure to get it looking and placed exactly where you want. —
For CSS changes, it’s a good idea to use a tool like firebug or Google Chrome’s built-in developer tools to locate them and then put the edits either in your child theme or in the “Custom CSS” option on your theme options page.
Also, here’s a helpful tutorial on how to use Firebug – http://vimeo.com/20917974. The only thing I’d suggest not doing is actually making edits to the theme’s CSS files, as it shows at the end of that video. However, the video serves as a good introduction to Firebug and how it can be used to find what CSS is effecting certain areas of your site without ever digging around in any files.