You can do this with a fine strainer in a bowl, some cheese cloth to line the strainer, and a lid to cover the whole draining rig, but I do this a lot, so I have a tool for it–also works great for salting and draining cucumbers.
This is a super-fine soft fabric sieve that fits in a draining bowl with a tight fitting lid. You can leave it in the fridge without getting stinky yogurt from the other things that might be in your chill-chest
And here it is filled with some yogurt with great active cultures. You get super-thick Greek-type yogurt up top, whey in the bottom. I got about a cup and a half of whey from this entire container.
This useful object, along with other delightful cultures, tools for fermenting, tips and recipes can be had from CulturesForHealth.com.