Suppose I fly to France and stay for 90 days. Then I cross into Spain by land, then fly to the Netherlands, then go to Norway. So the total trip length is much longer than 90 days. As long as I stay less than 90 days in each country individually, can I just take my American passport and not worry about anything? Or do I have to do some paperwork?
Basically you can stay 90 days out of each 180 days in the whole of the Schengen area. That is no more than 90 days for all the countries you mention.
There is almost no way to extend that when your whole stay is within the Schengen area.
You may have to adjust your travel plans or look for the very few loopholes that do exist.
The UK is not part of the Schengen area, nor is Ireland, which may give you alternative destinations to reduce your time in the Schengen area.