staying in multiple countries

I'm an American citizen and I'm planning on doing some school in a few countries consecutively in Europe. I don't understand what the 3 months in a country means (on an american travel visa guaranteed by a passport). Is it 3 months in each country, or a total of 3 months combined?
I want to spend 3 months in Spain, 1 month in France, and 5 months in Germany. If it is 3 months in each, then I suppose I wouldn't need a visa for Spain or France, just for Germany. But if it's 3 months combined, then I suppose I would need a 9 month schengen visa? or one for each country? If I go beyond 3 months in one country, does it mean I need a visa for the next country no matter how long I plan to study there, because I already stayed 3 months in a schengen country?
I am extremely confused about this. Any help would be greatly appreciated.
Thanks

ou est mon MD? J'ai besoin de l'information en vitesse.

I was away on holidays! I am back now.

You raise a complex issue, which has not found a harmonized solution yet amongst Schengen states.

To make it as simple as possible:

1. You do not need a visa for staying your first 3 months in Spain

2. According to a bilateral agreement between France and the US, youmay stay in France for 3 months even if you have spent 3 months previously in an other Schengen state

3. Regarding your 5 months stay in Germany, I guess you will need a visa. I would advise you to get in touch with the nearest German consulate.