See Serre in Motives vol, or Chapter 6 in André
See Toen AIM talk on Homotopy types of algebraic varieties, for a unified viewpoint on extra structure on Weil cohomology theories, and more.
http://mathoverflow.net/questions/71587/what-are-the-different-theories-that-the-motivic-fundamental-group-attempts-to-un
nLab page on Motivic Galois groups