Accented vowels help
There is no accented vowels on the Microsoft Greek keyboard. Not as far as I can find. I'm assuming there is a simple way to get these that I am missing.
I've been also just trying to figure it out for a while and and it's ";" + vowel (not simultaneously, click ";" first, then the vowel) on my keyboard (Linux). Maybe it'll work for you. If not, try googling descriptions of the layout. You're using a Greek layout from the settings, right?
I've just checked it on the other computer with Windows (what OS do you have?) and ";" + vowel works just fine in the default Greek keyboard. Try other possible Greek keyboard layouts. In the setting there should be a "+" next to "Greek". Click on it and you'll see the possible layouts. Add them and check if ";" + vowel is working on any of them. Especially try "polytonic" although I'm convinced it should work in the normal layout, too. Strange.
Mine works the way Gerardd88 says but when I was trying to figure it out I found a site that said to try "shift ;" and the letter. I don't know if it is all at the same time or what. http://www.patristica.net/graeca/how-to-type-in-greek/