Where do I get an Apostille in Greece or in the US

In Greece, you can get the Apostille from the government office that issued the certificate.

In United States, each state issues its own Apostille. The office of the Secretary of State will verify original documents that have been issued by a State agency as to its validity.

An Apostille can also verify the signature of a Notary Public for declarations, affidavits, sworn statements (υπεύθυνη δήλωση), Power of Attorney documents (πληρεξούσια – plirexoysio or plerexousio), authorizations (εξουσιοδότηση – exousiodotisi), wills, etc.