Digital Download Checkout experience is the same as any other shopping experience on your site, with one small difference, that you do not need to ship anything.
You can mange checkout experience with Checkout configuration. If customer cart has no products to ship, their shipping address request will not show up even if you configured it.
Once the order is completed and invoice is generated, based on your configuration, the customer is presented with a links to download the purchase. See a series of screens below.