Watch online Greek video lessons. Some are available from GreekPod101, which requires you to register (free). Several quality Greek lessons are available for free on YouTube as well (see Resources). Watch online Greek video lessons. One video source is on 5MinuteLife Videopedia. Write down new words that you learn from the videos. Practice those words every day. Listen for those words as you watch new videos. See how much you can understand from one video to the next.
Sign up on an online language exchange such as ITalki or My Language Exchange. Use voice and text chat to learn Greek from a native Greek speaker. Offer English lessons in return. Practice with different Greek partners on a regular basis so that you are producing Greek and listening to a native Greek speaker as much as possible and so you can listen to different speakers who might have different accents or pronounce words differently. Ask each conversation partner to help you learn new figures of speech and idioms in Greek.
Hire an online tutor to teach you Greek. Some independent tutors can be found on ForteMall, EduFire and Buddy School (see Resources). Online tutoring companies also offer Greek lessons in a small class setting or on an individual basis. Individual tutors can provide you with the attention and customized lessons you need to progress quickly in the language. Attend classes regularly and do so over a long period of time. A few classes over a few months are not going to help you become fluent. It is important to remain consistent in your studies, both independently and with a teacher.
Work through free online Greek lessons. Some are text, and some are audio lessons. Some resource sites include Kypros and Greek through the Internet (see Resources). Paid lessons are available online as well, such as those from I Learn Greek. Learn as much as you can from the free lessons first. Then, if you feel you would benefit from a course you pay for, move on to that.
Purchase a Greek language course from a bookstore or online. See if your local library has a Greek language course available for check-out.