In order to be able to write in Greek, two things need to happen. A mapping or layout of the keys of the keyboard to the corresponding Greek characters - this requires a keyboard driver - and a means for switching between different types of keyboard drivers are needed. Both requirements are accomplished as follows:
Under Start (or any other available means) go to Control Panel and run (double click) "Regional and Language Settings". Select the tab "Language" and under "Text services and input languages" click on "Details".
Under "Installed services" click on "Add". Select as "Input language "Greek" and pick the "Keyboard layout/IME" of your choice - the default is fine. Close the last window by clicking "OK".
In the "Text Services and Input Languages" window, under "Preferences" click on "Language Bar" and select "Show the Language bar on the desktop" so you can tell at any time which keyboard layout is selected for the application that is active. Click "OK" to return to the previous window.
Under "Preferences" click on "Key Settings" to open the "Advanced Key Settings" window. Under "Hot keys for input languages" make your selections for accessing or switching to a given keyboard layout.
People who use only two keyboard layouts usually just use one key combination to toggle between the two languages.
Under "Change Key Sequence" you can select the combination of CTRL + SHIFT or Left Alt + SHIFT, the latter choice being more common, for toggling between input languages. Close this window by clicking "OK".
Close the "Advanced Key Settings" by clicking "OK".
Close the "Text Services and Input Languages" window by clicking "OK".
Close the "Regional and Language Options" window by clicking "OK".
You should now be able to write Greek characters in most applications.