Required: Genesis Framework, Prose Theme
By default, only the left side of the header image links to the home page. The right side is a widget-ready area. To make the whole header image link to the home page (assuming you are not using widgets on the right side of the header), go to the Genesis > Design Settings menu and find the Header panel. Change the Header Title Area Width to 940 and the Header Widget Area Width to 0.
You cannot link to a page other than the home page. If you do not want the header image to link to anything, change the Header Title Area Width to 0.