When you successfully upload a file to an assignment you will see a green checkmark in the Submission window.  You must wait for that green checkmark.  Don't browse away from the page while your assignment is being uploaded:

If you wait, but don't get the green checkmark, here are some things to try:

  1. Clear your browser's cache & cookies.
  2. Update your browser to the latest version.
  3. Use Incognito mode, which disables browser extensions.  Chrome instructions.  Firefox instructions. As of 2017/1/16, the LastPass extension to Chrome is known to cause problems uploading to assignments.
  4. Try a different browser.
  5. Try a different computer.