Enroll in a beginner-level Greek language class. Find a Greek language class at a college, university, or language-training school such as Berlitz. Greek-language classrooms are the best place for beginners to learn the basics. There you will find essential oral and written assignments as well as an opportunity to practice basic speech.
Learn the sounds of the Greek alphabet. Listen to and repeat the entire Greek alphabet until you have it memorized. Doing so will help you pronounce Greek words. Though some letters appear similar to English ones, they may be pronounced differently or contain symbols that affect how they sound.
Practice enunciation of monosyllabic words and short Greek phrases as often as possible. Repeat numbers like "ena" (one), which is pronounced "EH-nah," and common words like "ohkee" (no) and "neh" (yes). Condition the muscles of your mouth to properly pronounce commonly used Greek sounds. This may cause temporary soreness of mouth and tongue muscles, but it is absolutely necessary.
Listen to Greek as much as possible, and embrace all opportunities to practice Greek speech, despite how little you know. Find and attend Greek cultural events in your area, such as festivals. Listening continually expands your comprehension of and ability to respond in Greek.
Watch Greek television programming if you live in an area with a sizable Greek population. Follow the network links in the resource section to watch clips of Greek television programs online if there are none in your area. Greek television is a good starting point for understanding simple Greek conversations and developing vocabulary. Hearing simple, fluent Greek in concentrated doses is invaluable to developing the comprehension necessary to speak Greek.
Immerse yourself in Greek by placing yourself in situations where only Greek is spoken as soon as you are comfortable enough to carry on simple conversations of your own. Find nearby Greek community events or plan a trip to Greece if possible. This is the fastest way to improve your ability to speak Greek.