It would turn thick and sour by itself. Today it is impossible because the milk has been pasteurized and will just turn bad. If you have access to unprocessed milk, than you can still do it the old fashioned way. But be aware, that the milk might be contaminated by other bacteria. The safest way is to buy processed milk and inoculate it.
Inoculation is nothing else but putting the right bacteria to the milk.
You can either buy the bacteria or start you own culture. He found out that certain microorganisms will cause fermentation. This is based on the killing of all bacteria in the milk. Now all milk you buy in the store has been pasteurized. The beginning of all cheeses is a soft cheese called Quark in Germany, which is nothing but thickened milk.