Three on-line papers are collected here, dealing with the geometry of paperfolding, which i've translated from English to hebrew with the authors' permissions. (the following three links lead to the English sources.)
Mr. Koshiro Hatori's How to Divide the Side of Square Paper describes procedures for accurately trisecting a square piece of paper by mere folding. Each procedure is followed by a mathematical proof of correctness.
Prof. Jeanine Meyer's Dividing into Thirds by Estimation describes an iterative procedure, by which a rectangular piece of paper can be approximately trisected to within an arbitrary degree of precision, by making several almost-identical folding steps, each of which approaches the desired goal a bit closer.
Prof. H. A. Verrill's Origami Trisection of an Angle describes a procedure for accurately trisecting an arbitrary angle, marked on a rectangular piece of paper, by mere folding.
Pleasant reading!