The short answer
Two cloths, one damp with glass cleaner and one dry, and wipe the inside horizontally and the outside vertically so you can tell which side a smear is on.
- Clean the inside first, which is usually worse. A film builds up from plastics off-gassing in the heat.
- Use an automotive glass cleaner or hot water with a drop of washing-up liquid on the inside.
- Two cloths: one to clean, one dry to buff.
- Inside horizontally, outside vertically, so a remaining smear tells you which surface it is on.
- Wind the window down a little to do the top edge, which is always missed.
- Clean the wiper blades with a damp cloth while you are there.
What will ruin it
Do not use ammonia-based household glass cleaner on a car with tinted film on the inside of the glass. It degrades the film and causes it to bubble and discolour.
Why it works
The inside film is plasticiser that has evaporated out of the dashboard and condensed on the cold glass. It is greasy rather than dusty, which is why plain water and a dry cloth never shift it.
Household chemicals can be dangerous in combination. Never mix them, keep the room ventilated, and test anything on a hidden patch first. Full disclaimer.