Code a custom nav/menu bar header for a wordpress site.

I have a wordpress theme that I need customized with a new navigation header bar. The nav bar would need to be coded from scratch. The goal is to add a bar across the top of the site/theme with a button that activates a series of dropdown buttons that act as navigation for the website. The bar/menu must be fully mobile responsive so that it will work on all cell phone platforms. All nav images have already been created and are accessible via the media library. I've attached two screenshots. The first is a screenshot of the top of the website as it is now without the nav, and the second is a screenshot of how the site should look with the new nav bar, and the buttons dropping down over the header image.