We know now that the placenta plays a big role in preeclampsia. We know this because not only does it resolve once the placenta is delivered, but there are also rare instances of a hyatiditiform mole (where there is no baby but placental tissues remain) and they can cause preeclampsia, too.
Basically, the placenta is not doing its job of nutrient exchange for some reason. It looks like that reason may be that the uterine lining does not relax enough to allow the placenta to implant properly. Specifically, there is not enough oxygen getting to the placenta while it is developing in the first trimester. The amazing placenta does its best at trying to compensate by branching its blood vessels and growing into odd shapes. It may help to think of preeclampsia not as a disease in and of itself, but more as a symptom of something not working with the placenta. Preeclampsia is also associated with diabetes, multiple gestations, and high blood pressure.
We think the problems the placenta has stems from inflammation and oxidative stress. There are many similarities between preeclampsia and atherosclerosis (hardening of arteries). It shouldn't be any surprise, then, to be able to see lower rates of preeclampsia in well-nourished populations. Specifically, changes that reduce her LDL levels. Vitamin C, Vitamin E, and iron probably also have a role. Certain types of fats are known to increase inflammation, like omega-6, while omega-3 has the opposite effect. Another recent discovery has been the influence of sleep apnea on this oxidative stress. If you snore or are excessively sleepy in the morning, you might want to talk to your provider about ways to improve your sleep.
Some recent studies have found these differences:
Women who develop early-onset preeclampsia drank more sucrose-containing soft drinks, and consumed more calories and polyunsaturated fats. 
Women who increased their calcium reduced their chance of developing preeclampsia by 32%. 
It occurred to me as I read through all the studies that all the supplements that show promise are easily available in a well-balanced, whole foods diet like I teach in my childbirth classes. Many pregnancy complications and health problems in general can be alleviated or reduced when eat plenty of healthy foods, yet the studies are trying to narrow it down to one thing that can then be supplemented in X amount in a prenatal vitamin. I really think it's much more than one nutrient we need or one type of food we need to avoid. So here's the bottom line for all women who are pregnant or will become pregnant in the future. The best way to prevent preeclampsia is to EAT WELL. It's not fancy or highly technical, but it makes sense when we think about what's most natural. Please don't put yourself in the position of having to deal with a preeclampsia diagnosis that can make you choose between your health and your baby's.