Here is the old-fashioned Lebanese method for yogurt-making I learned from my father. I remember he taught all our American friends to do this back in the 70s. I watched him and did it myself as a young teen. Still do every once in a while.
The Lebanese way to make yogurt involves no yogurt maker, cooler, thermos or any special equipment.
First organize your yogurt container. A glass or ceramic covered bowl or crock is best. I like those Corning or Anchor Hocking glass casseroles with glass lids, but a sturdy plastic container would do. Boil water and rinse the clean container and lid, let air dry.
Scald enough milk to fill the container - that means heat milk until bubbles form at the edge of the pot. Don't let it foam over, or heavens forbid burn it! Let cool until you can hold your (clean) finger in the milk for the rapid count of 10. About 110 degrees Fahrenheit I believe, but I never use a thermometer. (Update: Google is our yogurt making friend. Kitchen science link below says cool to 112-115; it will reach 110 when you add the starter).
Pour milk into your prepared container.
Stir up some yogurt in a cup. Let's say about a half cup for a half gallon of milk. This is the starter, which in our village we call the "rowbih." I pour a little hot milk into the yogurt, too, to bring it to temperature. You want to "break" the yogurt curds. Use a yogurt with live cultures, and don't use one that has pectin or gelatin (or anything else) added.
Then stir the starter into the hot milk and put the lid on. To keep yogurt warm, set container on a folded blanket or towel, and then wrap it up with old blankets, parka, whatever will keep it nice and warm. Let sit for 6 to 8 hours.
Over the years Americans have suggested all manner of ways to keep the yogurt warm. A haybox, if you already use one, seems like a simple solution; also I suppose a styrofoam "cooler" would also work but I have not tried this. If you already have a warming method you like, go for it. Personally I would not keep yogurt in an oven warmed to 200 degrees (F) for 6 hours - what a waste of fuel. But people do.
The yogurt should look firm and have solidified bubbles on the top. When it has set, refrigerate.
The kitchen-science, USDA-approved method. Includes non-fat dry milk powder, which many people can taste and don't like. OK it tells you to use a double boiler which makes it impossible to scorch the milk. Whatever.
Take your fresh yogurt, leaving some aside for another starter, and put it into a sterilized muslin bag. Add salt. Tie the bag shut and hang it from an olive tree branch. (Or your sink faucet, or anyplace else it can drain. Or put it in a colander).
Let drain until it's the consistency you like, from gooey to solid. Turn out onto a plate and drizzle with olive oil. Serve with olives, tomatoes, mint, cucumbers, and pita bread. Or eat unadorned with bread. But must add good olive oil.
Alternative draining methods I have seen include using coffee filters, layered cheesecloth or even paper towels in a colander.
Your own olive oil from the tree where the lebneh drained would of course be optimal but even Lebanese can't achieve that too often. Most of them buy their lebneh in plastic tubs like the rest of us, these days.