The general idea of the Paleo diet is that we (humans) have not really evolved that much over the past 10 000 yrs or so and that our bodies are yet to catch up to the agricultural revolution. i.e humans farming and no longer being hunter/gatherers.
The basic Crossfit prescription for nutrition is, more or less, a Paleo approach "Eat meat and vegetables, nuts and seeds, some fruit, little starch and no sugar."
A good approach is: If man made it - don't eat it! There's a long list of whats allowed and not allowed on Paleo, but to be strict about it, it is: No grains - rice, oats, wheat products. No Dairy. No caffeine. (But some authors apparently say in moderation caffeine is ok - DAN!) No alcohol. No starches - potatoes, sweet potatoes. No legumes - beans, snow peas, peanuts. I think that covers most of the no's.
This is the place for your questions: http://www.thepaleodiet.com/faqs/ It has stuff about calcium, fibre, fat, cholesterol.
This is another simple run down, it has links (scroll down) to download a list of foods, recipes and a shopping list: http://www.sbs.com.au/shows/foodinvestigators/listings/detail/i/2/article/2949/Episode-3-The-Paleolithic-Diet You can also watch episodes and see how the people cope and what they say about the diet. Plus you get to see my creepy internet crush, Renee Lim... whoo
Again, Robb Wolf has answers: http://robbwolf.com/?page_id=121
A bit more on what not to eat: http://lowcarbdiets.about.com/od/paleodietcavemandiet/a/paleoforbidden.htm
It is restrictive, and hard in many ways. Personally I've been trying to stick with it for months - but never entirely. How could I give up peanut butter! How could I give up oats or snow peas! Only in the last week have I gotten serious about Zone and Paleo (still milk and tea though..don't think protein shakes are paleo either) Some say you have to be 100% strict, others allow a bit more leeway, either way - the more you head down this path the better your health outcomes will be I think. Even if its just getting rid of those processed carbs.

