Mozzarella is a cheese, traditionally without bacteria cultures added. The traditional Italian mozzarella is made of buffalo milk but it can as well be made from goat's or cow's milk. I personally have only made goat's mozzarella.
First the milk is usually pasteurized: It is heated for some minutes to 72 ºC (~92 ºF). Then it is left to cool down to some 25 ºC (~77 ºF), it is added rennet to (quantity according to product information) and is left alone at least half an hour. When it is curdled, it is cut into small pieces and put in a clean cloth so that the whey can drop out, the cloth is closed with a cord and hung up. Below we put a container to catch the whey.
After some twelve hours the mozzarella is taken out of the cloth and put in the whey (or in salt water) antil it is used.
Mozzarella is meant to be consumed within a few days. It does not conserve well like a real cheese but is rather a fresh cheese.