Hi,
Create a child theme first, as you might want to change more stuff later.
Upload your banner to your wp media library.
Then put this in your child theme css:
#header
{
background-image: url("https://yourwebsite.com/wp-content/uploads/2015/02/yourheader.jpg");
}
You might want to tweak some more stuff and add smaller banner images to have the responsive thing work more smoothly for your header, but this is a start I think.