If you want to make your own cheese at home it's actually very simple. I like making my own fresh ricotta and mozzarella whenever I need it (like for lasagna or pizza). Once in a while I take a drive to a farm and get a gallon of fresh milk from them. I don't like using store milk for this because it's already been "altered" but if you don't have a choice then go for whole milk and the one that doesn't have extras like vitamin D or calcium add-ons.
First ricotta - simplest possible cheese. Poor milk into a stainless steel pot or use other non-reactive pots for cheese (don't use aluminum!), add about 1/2 cup of vinegar, a little salt if you want it, and bring to about 200 degrees. It will be almost to a boil but not quite boiling yet. Keep stirring so it doesn't stick to the bottom. Then let it sit for about 15 min without touching it. You will see separation of curds (white fluffy stuff) from whey (yellowish liquid). Pour mixture through a sifter or a cheese cloth and let curds drain well. That's your ricotta. If you like your cheese smooth you can add a touch of cream and mix it well.
Now for mozzarella - you will need milk, renet, citric acid (you can find both in a grocery store), cheese cloth and non-reactive pot and a thermometer. First chill your milk to about 50 degrees. Take 1 tea spoon of citric acid and dissolve it in 1/4 cup of water. Dissolve 1 tablet of renet in another 1/4 cup of water. If you have liquid renet then use 1/4 tsp. Take another 1 tsp of citric acid and put it directly into the milk. Add 1 tsp of salt. Acid is what will give your cheese elasticity but it has to be used when milk is cold. Then bring milk to 88-90 degree slowly on very low heat. Make sure it doesn't go past 90 or renet won't work. Add renet to the mix, stir quickly for few seconds and walk away! Let it sit undisturbed for at least 20 minutes. You will see curds forming and separating from whey and clumping together. Take a sharp knife and cut into strips first one direction and then another so it's almost like cubes. It should not look like ricotta! Cubes should be pretty firm and bonded together. Now bring it up to 105 degrees so it binds even tighter. Take a sifter and line it with cheese cloth, use slotted spoon to take out pieces of cheese and let them drain from whey. Try it for salt content and add more if you like it. Place cheese into a glass dish and put into microwave for 15 seconds. Then knit it with your hands like you would work a dough until it's nice and smooth and shiny. Blast it in microwave again if you need more flexibility. You might have to do it several times to achieve results. If it's too hot to handle with bare hands use latex gloves. Shape it into a ball and dump it into ice cold bath for a quick dip to set the form. You got your cheese.