You probably already figured this out, but after you enable the Greek Polytonic keyboard as Nathan mentioned, you need to look in the same menu at the top right (where the enabled keyboards are listed) and click on Show Keyboard Viewer. This puts a mini keyboard on your screen. You can use it with any installed font that handles polytonic Greek. You can even click on the keys and have the characters appear in your word processor.
Another good option is the Tyndale kit which includes the Cardo font and keyboards for both Greek and Hebrew, and a PDF showing the keyboard layouts. You can get it here: http://www.tyndale.cam.ac.uk/index.php?page=unicode
P.S. It's fun to try writing messages in Greek too. You can PM me in ancient Greek if you want to practice. I'm a beginner at that, but it's fun trying.