I think it's important to add that the research of Wolfgang Lutz ("Life Without Bread") was done, before we knew anything about the glycemic load (GL) and the glycemic index (GI). He created all carbohydrates equally, but today it is obvious that it is a difference if you eat 72g of pure sugar or a few hundred grams of for example sweet potatoes or buckwheat. But after reading about his successful treatments it's good to orientate on the amount of 72g anyway.
Lutz noticed that 72 g of carbohydrates is the amount which your other organs besides the brain need and process during 24 hours completely, so it can't affect insulin or blood sugar level. (I don't have the book at hand, I think this was the basic point)
The thing is to reach the state of ketosis, where your brain changes from the use of sugar (all carbohydrates) for energy to the use of ketone bodies. The difference is that the liver stops the processing on the level of ketones, instead converting it into sugar, because when you have a low intake of carbohydrates you aren't able to live on sugar (gucosis) anymore. So that you don't starve to death, the body begins to convert fatty acids into energy.
This is a really interesting topic. There is evidence that migraine or other neurologic brain disorders (and every insulin related disease like diabetes, arteriosklerosis, heart attacks, obesity, etc. anyway) can be healed with ketosis because these disorders are related to problems with energy-crisis due to the high sugar intake and insulin and blood sugar variations. The body just needs to much glucosis too fast.
Using sugar for energy means after a few hours of burning glucosis you need more of it, because it is consumed very fast. This is most of all the case with high-glycemic foods that make blood sugar level (and insulin) rise and fall in astronomic areas. Switching to ketosis means you can use the ketone bodys for hours or even days without having to eat because it is a slow metabolism. This is the reason you eat less on a low-carb diet. Without the variations in the insulin or blood sugar level you have a constant supply of energy.
The way to get there is to eat enough proteins and fat and almost no carbs, especially no carbs with a high glycemic load. The high fat amount is necessary because otherwise the body uses it's own fat savings and you get protein toxicity.
It is important to adjust and not to switch cold-turkey because during the days before ketosis your body is starving. In this phase of transition your body hasn't enough glucosis to live on but still isn't able to produce keton bodys. This phase can be accompanied with energy-crisis like migraines if one doesn't adjust properly.
Like Laura said, Lutz had a lot experience on that and he also noticed that for really ill men over 50 and woman over 45 (or something like that) it is impossible sometimes to switch to low-carb at all due to the fact that the body is adjusted to the bad lifestyle and cannot change anymore without serious problems.