This has a drawing that might help:
http://sewing.about.com/od/beginner1/p/fabricgrain.htm
I prefer to make my first cuts parallel to the selvage - because then I figure at least two edges of a right angled quadrangle piece will be on the straight of grain.
By the way - there is crosswise grain AND lengthwise grain.
Generally, the lengthwise grain (parallel to the selvage) is less stretchy than the crosswise grain.