We have received other questions from people doing octagon-shaped carpentry (take a look at this quandary or this other one). They help you figure out just how wide the sides should be. How you do your cuts will dictate the actual board lengths themselves (for example will the boards be parallel to the side of the octagon, or parallel to the corner-to-opposite-corner?).
As to how much lumber it will take, you need to look at the area of the octagon, which is described in this question.
You are using dimensional two by sixes, which are in actuality just 5 ½ inches wide. To that, you add your ½ inch spacing to get a real 6 inch width. That's half a foot, so if you divide the area in square feet by this (or multiply the area by two), you'll get the linear feet of lumber it requires.
Note however, that this doesn't take joins or angle-cuts into account - so you'll need some extra to account for the angles you are cutting off.
Hope this helps,
Stephen La Rocque.