Activating your copy of Papers requires an active internet connection. If you don't have one, or your institute blocks our website, follow the instructions that are presented to you on a Mac by clicking the activate while holding the alt/option key, or on Windows by going to Settings Activate > Manual Activation. This will bring up a dialog explaining how to manually activate your copy of Papers.
You will need to save an activation request file that you can upload here from a computer with an internet connection. This then allows you to do download an activation code file and you need to bring back to your computer. On Papers for Mac drag the activation file onto the Papers icon and on Papers for Windows use the Import-button on the manual activation window to import the activation file. This should now activate the program.