You need high quality goat milk for a superb goat cheese. You really do need raw milk, store-bought is no good.
Put a large pot on the stove, pour the milk in it, turn it up to moderate heat. Grandma told me that it needs to heat up to about 98.6°F (37 °C), without boiling but I didn't want to take any chances and heated it to 140°F (60 °C) to pasteurize, then I let it cool to 96.8°F (36 °C).
If you don't have a thermometer, you can dip your finger in it and try it - you need to be able to withstand the temperature.
Next comes the yeast. I followed grandma's instructions to the letter here. Cheese yeast is sold in liquid form in small bottles in large supermarkets. On the bottle it says how many drops you need per 4 1/5 cups (1 L) of milk - in my case it was 5. You can measure out 20 drops but grandma told me that 1 tbsp of the yeast per 1 gal milk would be fine.
So, once the milk cools down to body temperature after taking off the stove, add 1 tbsp of the yeast to it. Stir with a wooden spoon but only from the top down and sideways; don't stir in a circular motion. Leave as is for 5 min. and cover the pot with a lid.
Prepare 2 thick blankets.
Cover the pot well with the blankets to keep the heat in and leave it that way for 1.5 - 2 hours, without touching it.
After 1.5 hours, remove the blankets from the pot and leave aside to cool a bit for 30 min.
Take the lid off the pot - at this point a white mass will have formed, with the whey separated around it. That's exactly what needs to happen. So far, so good.
Take a knife and cut the white mass into pieces, don't worry about them mixing with the whey.
In another pot, place a large piece of cheesecloth, pour everything in it. The whey will drip down, while the cheese will remain in the cheesecloth. Tie the ends in pairs and hang it up on the faces to drain. It will take about 2 hours to drain. Once it stops dripping, take it off the faucet, wrap the cheesecloth tightly around the cheese, place in a large plate, put a wooden board on top with something heavy on top to press down. I used a large bag of flour and jar of honey. Press well and leave it that way for another 3 hours. It will continue releasing liquid during that time, so be sure to periodically pour out the whey at the bottom.
Once the time's up, remove the weights, unwrap the cheesecloth and you've got yourself a wonderful white, soft, creamy goat cheese.
Cut it into pieces, sprinkle with coarse sea salt, including in the cuts, and leave in the fridge for 1 hour.
Your cheese is now ready to eat. You can make a brine of water and sea salt and put it in it to mature. In my case I eat it all within 2 days, so I don't need brine. Homemade cheese really is worth the extra time invested.