Only Verified Users can change the Cover photo (Banner) of their profile.
You'll first need to go to your Timeline. At the top of the page, above your Profile Picture, is the space in which your current, default Banner can be seen. To change this, select the Camera icon in the corner of the Banner.
Just like for the Profile Picture, you'll be redirected to a new page, from where you can Upload a new image or Choose from already uploaded photos. Keep in mind the image has to be big enough to fill out the entire space, for it to be a valid image.
From the same page you can choose to Edit your current banner, or delete it.
Check out our article to find out how you can get your profile verified!