To make yogurt cheese simply pour your yogurt into a cheesecloth bag or a colander lined with cheesecloth and suspend above a container to catch the whey that will separate out. I put mine into a cheesecloth bag and then suspend it on a sturdy spoon in a gallon glass jar. The gravity pulls the whey out and in about a day you have the finished yogurt cheese. I always keep it in the fridge to keep it cold as the whey strains out.
You can see the whey here dripping down. After the cheese is ready I store it in Tupperware in the fridge. You can mix in all sorts of things like lemon juice and chives, garlic, mint, tarragon. Or whatever seasoning please you.