How do I obtrain an eu passport as an american-

You need to become a citizen of an EU country. Every EU country has different rules. For example, if you have a parent or grandparent who was born in Ireland, you can establish Irish citizenship for yourself. If you have a parent or grandparent who was born in Italy and if you were born before your parent became a US citizen, you can become a citizen of Italy and then apply for an Italian (EU) passport.

If you have no connection to an EU country (maybe your ancestors came over on the Mayflower), the only option I can think of is to marry an EU citizen and live in that EU country for the required number of years.

How do I obtrain an eu passport as an american-
Those are definitely the easiest ways. You can also naturalize in a few countries as well, if you don't mind learning local language and customs