It's fun, isn't it? I got a huge charge out of learning about that, when I needed to add umlauts to a, o, and u in German. ä (alt+0228), ö (alt+0246), ü (alt+0252).
One way to find out the numbers you need to type in is to start out in a word-processing file, click on "Insert>Symbol" and then look at the bottom of the dialog box for the shortcut key, which will partly depend on the font you have selected.
You probably could use this feature with your Greek teaching, because the Greek alphabet is available this way! Here's another rush: in a word-processing file, type in 04E8 then immediately alt+x. Be sure the x is not capitalized. (This does not work in this reply-box, by the way.)