International Living Community

Weve been working on the same issue for my husband for several years The place to start is rhe Greek consulate in your area- theyll have a checklost for you. First thing will be to get all your papetwork in order- certified copies of all birth, marriage, and death certificates. Get them apostilled at the Sec of State in the state of their issuance, get them translated by a translator approved by the consulate. Get an FBI background check. Get your passport apostilled and translated.
Concerning the previous comment regarding getting you family "registered" in Greece according to where your grandparents are from... we are just learning anout this step ourselves (the LAST task for us) so cant comment about that yet.
And if your husband doesnt speak Greek its time to start studying... weve heard they will require some sort of evidence of his "Greekness"- language, culture, knowledge of history/current affairs etc. This part is not spelled out in our consulate communications but weve heatd this from other sources. They are raising the bar on citizenship so its not as easy as it used to be. Good luck!