I just began doing Greek Yogurt this year and we LOVE it. I'll never make it without draining again.
I've had the most luck with letting the yogurt completely cool down in the fridge after it's made before draining. After cooling, I put it in a butter muslin (cheesecloth) lined colander then tie it in a bundle and hang it just like you would for draining a soft cheese.
Length of time draining is a personal preference depending on how you like it. I've also found that if it was drained too long and got "drier" than I like, I've been able to stir a bit of the whey back into the yogurt to make it the consistency I do like so it's pretty "forgiving".
If you're like me, once you try this you'll probably never do it any other way it's SO GOOD!!!!!
FYI..
I make my yogurt at quantities of 1-2 gallons at a time by using one of my ss stock pots. To incubate, I put it in a large styrofoam cooler (since we had it laying around) which is tall enough to put the whole pot in. It won't fit the lid, however, so I just put a sheet of plastic wrap or foil over the top to cover.
To keep the temp up, I put near-boiling water in a couple of 1/2 gal canning jars that I can lay down in the cooler beside the pot without touching the pot. To watch the temperature I use a digital "meat" thermometer with the probe inside the container and the base sitting on the top of the cooler where I can see it. (I've also just used a regular thermometer and checked from time to time but opening the lid drops the temp.) I change the water with new hot water as needed to keep the correct temperature.
Hope that's hellpful!