You can use a sponge and soap, or easier yet, a pressure washer, to get any debris and algae off your dome. It will come nice and clean again even after years!
Sometimes, there can be soot from the chimney that leaves grey streaks which are a bit harder to clean and may require some scrubbing with soap or bleach.
Scrub the window with a non-abrasive sponge and soap or window cleaner.
If you have the pleather liner, you can clean it with a damp cloth and soap if needed - make sure not to scrub too hard.
Our new Oxford Fabric liner comes in multiple sections that can be machine washed.