There are no placement agencies.
You need to secure a work/residence permit as a non-EU citizen just like everyone else. She has a lot of information for non-EU citizens (and everyone, actually).
http://americaninat...residence-work-permits/
Apply for jobs just like everyone else, just like in your own country. Lots of good articles and links on her site:
http://americaninat...ategory/jobs-in-greece/
No one is going to just give you a job without doing your homework, having qualifications and submitting an application/CV just like everyone else in Greece.