U.S. citizens do not need a visa for tourist or business travel to Poland. Any U.S. citizen who wishes to travel to Poland for any purpose other than tourism or business negotiations (e.g. work, study, adoption, immigration, or stays longer than stipulated in the entry requirements) should contact directly, the embassy or nearest consulate.
A Schengen visa issued by an Embassy or Consulate of Schengen states allows the holder to travel freely in all of these countries.The period of stay for US citizens visiting the Schengen states is a total of three months cumulative stay in the combined member states during any six months period.
Since you are going to stay at least 9 months in Poland you do have to contact the nearest consulate. If you are US born but your parents or one of your parents is Polish citizen you are Polish citizen and you can apply for Polish passport.
What if an American wants to be there legally and work.....what kind of visa would they need and how would they apply for it?
You will need a work and residence visas.
Work and residence visas for U.S. citizens are free of embassy charge.
contact the embassy or nearest consulate.