It's so easy.
...and it's inexpensive. Milk is as low as $1.99 for 16 cups, compared to $2-$5 for four cups of store bought yogurt. So, the worst case is that your yogurt is going to be one quarter the price of storebought. And, storebought at that $2 price often has thickeners
...and if you like Greek yogurt, you can do that, too. Greek yogurt is very expensive, and this isn't.
Things you need.
Small container (6 or 8oz) of plain, active culture yogurt - you really only 4-8 tablespoons, so you can eat the rest
Big carton or jug of milk - skim, 1%, 2%, or whole is up to you.
Big heavy pot
Flame Tamer (optional)
Candy thermometer (or some way to tell when the milk reaches around 190 degrees and cools to 125 degrees)
Containers for storing yogurt (I make 16 cups of yogurt and use four 4 cup plastic Glad containers). Sometimes I used eight 2 cup canning jars and lids.
Oven with an oven light
Slowly heat milk in the heavy pot until it reaches 180 degrees. If you have a flame tamer, use it to keep from scorching milk to the bottom of the pot. As it approaches 165 degrees, stir occasionally, but try not to touch the spoon to the floor of the pot, since there may be a milk 'skin' down there. You really want to leave it there, untouched. When your milk is 180 degrees, remove from heat and allow to cool until it reaches 125 degrees.
Spoon equal portions of yogurt (starter) into each of your jars or storage containers. When milk reaches 125 degrees, ladle or pour some milk into each container and stir to combine. Ladle or pour remaining milk, equally, into the yogurt containers. Stir gently to mix. Wipe container edges with a clean paper towel, and put the lids on the containers.
Place them in the oven and turn on the light. I've used all sorts of temperatures, from 80 degree 'room temperature' to 95 degrees in my oven with the light on. As long as you keep it under 115 degrees, it should be okay. Cooler takes longer to firm up.
Anyhow, back to the oven... Place them in the oven and turn on the light. Wait eight hours, then place yogurt in the refrigerator, because it's done.
I'll call it strained yogurt, since this isn't Greece.
Line a collander with a very clean and fresh bandana, cloth napkin, or handkerchief . Cheesecloth is too loose without using a million layers, so don't bother. Pour in some yogurt, place in a large bowl that leaves room underneath the collander for the draining whey. Cover the yogurt and bowl with plastic wrap or a large plate to keep some of the moving fridge air out. Stick it in the fridge overnight. In the morning, you'll have strained yogurt like the Greek stuff.
For smaller batches, I use a drip coffee filter basket and filter over a mixing bowl.
For thicker stuff, like yogurt cheese, after you're already at the "Greek yogurt" stage, twist that bandana up so you have a ball, and place something heavy on the ball of yogurt for a few hours, or overnight, to press more liquid out.