Sign up for a course in Greek at a local college or private language school. Consult your local business directory to find a provider near to you. There should be a number of schools offering tutelage in Greek in most major towns and cities in Greece. If you can't find one, try visiting the websites of international language school brands like EF or Berlitz. Some of these services offer distance courses over the Internet.
Watch a lot of Greek television. Alternatively, watch English television with Greek subtitles or vice versa. This is a great way to get a feel for how the language works outside of the confines of a learning environment.
Speak Greek whenever you can. You're likely to come across many people who are happy to speak English in Greece. Always insist on speaking Greek once you're confident enough to carry out basic conversations. Immerse yourself in the language.
Navigate to websites like Kypros.org or Agni.gr. Services like these offer basic online lessons in Greek for beginners. They're a great way to ease yourself into the language if you're a complete novice. You can also order Greek self-study books from sites like Kyknos.com and Greek-language.com or CD-ROM-based courses from companies like Liguaphone or Rosetta Stone.