I was born in Greece and I have been a US resident (green card holder) for 7 years.I have my biometric Greek passport that was issued May 2007 and expires May 2012.How do I get a new one after the old one is expired?

You can either get this done in Greece on your next trip there, or in the USA at one of the consulates [New York, Boston, Chicago, Atlanta, Tampa, Houston, LA, or San Francisco]. You will need your Greek taytothta, two Greek passport photos [the consulate will tell you where you can get them issued in the city where the consulate is]. The cost is about $100, but changes every month based on the exchange rate between EUR and USD. The passport takes a few weeks to process. If you need it immediately, you have to go to Greece and you can have one issued there within three business days.