Updates
The Web Edition keeps itself up to date. The App Store Edition gets its updates from the Mac App Store, like any app from there.
Checking automatically
Once a day, PanoPaper checks for a new version by itself. It never interrupts you with a window: when it finds one, a small red dot appears on its menu bar icon, and 'Check for Updates…' in the menu becomes 'Update to version…'.
Choose it to see what's new and install the update; PanoPaper then restarts on its own, cameras and all.
To stop the daily check, turn off 'Check for updates automatically' in Settings ▸ General ▸ Updates.
Checking now
Choose 'Check for Updates…' in the menu bar menu to check right away, whether or not the daily check is on.