Learn online. There are numerous free online Greek language courses on the Internet, including Kypro, Word2Word, and LiveMocha. The main advantage of online courses is that they allow you to practice whenever you have time available. As you decide which course to choose, consider how you best absorb information. For example, if you learn best by reading, pick a course that offers primarily teaching via visual material. If listening is your strength, then choose a course with audio lectures. To learn Greek well, you will eventually need to learn through both reading and listening. However, when you are just starting out, go with your strengths.
Go to the library. Your local library is likely to have Greek language books, CDs and DVDs that you can use study. The library may even have Greek movies (subtitled in English) that you can borrow. Use these materials in addition to any online course that you may take. The more you immerse yourself in the Greek language, the faster you'll learn it.
Talk with native speakers. Learning to speak Greek well requires that you talk and listen to native Greek speakers. You may be able to meet mother-tongue speakers willing to talk with you at Greek community centers or local churches. If that doesn't work out, think about joining an online language exchange program. My Language Exchange is an online program that arranges for you to exchange a certain amount of time practicing Greek with a mother-tongue speaker for an equivalent amount of time speaking in your native language.