Adding a search box to the primary menu of your Genesis theme is pretty easy, thanks the latest version of Genesis. If you still need a hand, this guide can help.
Although this guide uses the Genesis Sample theme, you could make it work for any other Genesis child theme with some minor tweaks.
If you’re using an older version of Genesis Sample theme such as Genesis Sample version 2.3.0, you need to add the following code to your functions file and stylesheet respectively.
Are You Using Genesis Sample Version 2.6.0?
If you’re using the latest version of Genesis Sample theme such as Genesis Sample version 2.6.0, you need to add the following code to your stylesheet and functions file respectively.
Note: You might need to make some minor css tweaks as per your current theme. As for the CSS, you can either use the code in WordPress customizer or search and replace the properties in your child theme’s stylesheet to avoid any potential override. It’s completely up to you.
Hope this helps. Let me know if you have any questions.