You should go to the site and download the ebook and you can begin reading the recommendations right away. Loren Cordain, PhD, the main researcher, puts it more elegantly than I ever can, and is more knowledgeable than me.
The diet is basically the Paleo Diet (
Paleo Diet, The Paleo Diet, Paleolithic Diet, Caveman Diet, Hunter Gatherer Diet - dedicated to Paleolithic Nutrition and the Science of Healthy Eating) with some minor modifications.
If you had specific questions it would be more helpful, however I can try and think of a general overview. Science:
An omega 3:6 ratio that is out of balance causes inflammation, that exacerbates already existing acne.
Hyperinsulinemia from eating foods high on the insulin index and glycemic index cause a negative endocrine response in two ways: IGF-1 is increased and IGF-1 binding protein is decreased, leading to keratinocyte (skin cell) hyperproliferation.
If your skin cells proliferate in an abnormal and out of control way, and they are overly adherent (stick together instead of dying off in a normal way) they are what cause acne when they block the pore. They don't die properly, and instead hang around for a while.
You will have slightly increased androgen levels from eating high GI foods, which will lead to a greater production of sebum (oil). This is what fills the pore after the overly adherent keratinocyte desmosomes get stuck together.
Eating foods with certain inflammatory lectins that enter the blood stream through the back door of cells in the gut. Normally proteins break down but these are resistant for some reason. They enter the blood stream and cause an immune response that has been implicated in the high level of autoimmune diseases in the Western diet compared to modern hunter gatherer tribes. The acne relevant part to this is that they alter the structure and adherence of skin cells, thus causing them to stick together more (if I remember correctly). You will have to check this part in the book.
Those lectins are contained in foods you have been eating, such as any grains or lentils. The brown rice, pasta, and peas you eat have them.
If you look at modern day hunter gatherer tribes, they have zero incidence of acne. It is only until the Western diet is introduced, with cereal grains and other staples, that they begin to have acne. Several comparisons of tribes have been done in scientific journals in this way.