On Submittable, in My Submissions, find the submission you want to download. Click on the submission title. This will open up the submission's details page, where you can click the Download button in the upper right of the viewing box

When you click Download, a .PDF summary of your submission will be downloaded to your computer.
If you wish to download individual files from within your submission, scroll through the submission until you find the file you want to download, then hover over it and you will see a download icon appear. Click the icon and that file will download to your computer.

For more information, https://submittable.help/en/articles/2814108-how-can-i-download-a-copy-of-my-submission