Greece has slowly tightened implementation of its obligations as a member of the EU Schengen Group on immigration. American passport holders used to be able to stay in Greece indefinitely, provided they left the country every three months, and authorities were lenient. Now, legally at least, Americans can stay in Greece or any other Schengen Zone country no more than three months in any given six-month period, and then must launder themselves through three months outside the Schengen Zone. Otherwise, they must acquire a Greek residence permit. The U.S. Embassy web site has useful information on residence permits at http://www.usembassy.gr/consular/ac_residency.htm
In most cases you must get the appropriate Greek visa from a Greek Embassy or Consulate outside Greece before you can apply for a Residence permit. If you plan to work, you will need a work permit as well, with documentation from your employer ready in correct form at the time you apply for the visa. It is relatively straightforward to get a one-year residence permit without the right to work, if you can document adequate resources to support yourself.
Be warned that Greece's Residence Permit situation is in disarray, with long delays as the bureaucratic football gets kicked between the local municipality, the Interior Ministry (represented by the Periferiarch of the broad region), the Ministry of Labor and Social Welfare, and the Ministry of Public Order. See the excellent articles by Kathy Tzilivakis on the new law, published in the Athens News in December 2005 and January 2006.
The Athens Municipality center for foreigners is a set of rooms on Maizonos between Chiou and Psarron (two blocks north of the Metaxourgeio Metro station). Once the municipality has accepted your application for transmittal to the Periferia, it will give you a white piece of paper with your photograph and protocol number. That, with your passport, is proof you you are legally in Greece.
The new immigration law passed in 2005, along with instructions and permit application form, is downloadable, in Greek only (as of 9/05), at http://www.ypes.gr/allodapoi/content/GR/default.htm
An English-language guide to the old law, but with useful addresses and phone numbers, is at http://www.migrantsingreece.org/transpartner/GuideEnglish.doc
If desperate and unable to afford a lawyer, try:
Network for Social Support of Refugees and Immigrants Information and Support Office Tsamadou 13, Exarchia.
Open Monday-Friday 5 p.m. to 9 p.m. Shelter open: 8 p.m. to 1 a.m.
They provide legal service, Greek lessons free to low-income immigrants and emergency shelter placement. Low-income clients are served free; higher income clients may be referred to private services. They are building their expertise and a good network. They also advocate for proper implementation of existing laws and changes that would enhance the immigrant experience.
Click here for tips on bureaucratic comportment and where (in 2004) you could get your Greek Health Certificate.