Egg Tempera wasn't really established until the 13th Century. Until then, people had used a variety of mineral and earth pigments such as Umber, which has been around for a long time. The process to making Umber is rather simple. All it is is mined earth that has been washed, dried, and ground to powder. It can be used raw, which gives a yellowish tint, or roasted to give a brown-red colour. There are other pigments that can be found anywhere, as well. Such as the colour Lime White and it's process is just as simple. Simply take some lime stones, and have them soak in a bucket of water for eight days. You also have to change the water out every day, though. Once it's finished soaking, dry it out, grind it into powder, hydrate it, and there you go. In some cases, stones were used in the process of making paints. Such as Malachite and Azurite.

One other way, and possibly the most dangerous, of making paints was the use of Lead. This is under the category of "Manufactured Pigment", whereas the paragraph before was more towards Earths and Minerals. A manufactured pigment is just a pigment that has been processed in order to gain a new colour. It's also dangerous, I wouldn't recommend it, to be honest. Anyways, one such process is for Lead White. Since classical times, this pigment was created by placing strips of lead over a vase of vinegar and/or urine, which is then sealed and placed into a dung heap for several days. After a few days, the artist(s) would then scrape off the formation around the seal, and grind it for use. Lead is a poison, and must be handled with care at all times, however, back then men and, especially, women would place lead based pigments onto their skin for cosmetic reasons.

Sources:

• Common Medieval Pigments PDF

• Egg Tempera Recipe

• Pigments Through The Ages (500 - 1400)