You could start by having a look at Post Thumbnails and how to enable them for your theme. You will need this to enable the functionality of setting a featured image for your post. This page is great for learning lots about how Post Thumbnails in WordPress work, you should really read all of it.
You will then most likely want to add a new size for your “top banner thumbnails” by using add_image_size(). This helps you to define new image sizes, which WordPress generates when a file is uploaded. Images can be cropped or resized to fit your size. This takes care of having images which are 1920 x 350 pixels large.
Finally you will have to create some kind of markup, either for a background image or whatever, and will need to output your top banner image. Using get_the_post_thumbnail() or the_post_thumbnail_url() and passing your new image size as a parameter can help you with this.