There are quite a few recipes out there for making your own mozzarella. I don't remember which one we used, but I don't think it's terribly critical, since it was wrong. :-)
Basically we added some rennet, (found at grocery store), citric acid (found at health food store), and milk together in a pot, and heated it up. The instructions that I found bookmarked on my phone (best guess as any, but I think we ended up combining several recipes) say to combine 1 gallon milk and 2 tsp citric acid and heat to 88 degrees F. Then, add 1/2 tablet of rennet (dissolved in 1/4 cup chlorine-free water), and heat it up to 105 degrees F. The directions then said to turn off the heat and large curds would appear in a sea of clear-greenish whey. This did happen for us, but we had to wait several hours before the curd was firm (slice-able), and the whey was clearish.
Now the fun begins! We drained the whey off, and pressed the curd to get as much whey out as possible. (it was hot!)
(I saw a recipe on the insert that came with the rennet that said you can make a different type of cheese out of just whey...so you can always save it! My thought was you could maybe sub for liquid in bread... could be sourdough-y?) At this point, we followed the recipe to microwave for 30-second or so increments, pressing and draining the whey out in between.
After about 3 of these, we could start kneading the curds. It was tough going at first with the kneading, as the curds really didn't want to stick together, but we kept at it.
The curds actually got rather bouncy, like pizza dough. (we had to reheat the whole mess several times to keep kneading--otherwise the curds stopped sticking to each other).
When it felt and looked like a ball of mozzarella, we figured we were done.
We formed the ball of curd (now cheese) into two balls, put them in a container of salt water (later we learned that a little goes a long way and mozzarella soaks up whatever you keep it in--note if you go too far with the salt just soak it in plain water for a while) and stored them in the refrigerator. According to what I read, the fresh cheese will only keep about a week.
I promise I'll take more reliable notes next time! (cheese-making is messy)