So here's what you will need:
Greek yogurt is just plain old yogurt that's been strained to get the whey out of it. Since I didn't have a cheesecloth, I used a piece of thin fabric. Yes, I know, improvising again. It worked pretty well, although you will probably get a creamyer (is that a word? LOL) ice cream the more whey you strain out. I hung the bag from the microwave with a bowl underneath to catch the whey. Pigs, goats, and chickens love the stuff, so feed it to them if you have any!
The ideal "Greek Yogurt" should be the consistency of cream cheese, or slightly runnier.
Mix in the sugar and vanilla, and refrigerate it for 45 minutes.
Pour mixture into the machine, and continue following the manufacturer's instructions.
Now you have a relatively healthy sweet treat! ;-)