Google search linticular designs. Youll find tons of info. Art and printing are extremely hard. Im still trying to figure the art out. The printing is a whole nother ball game. Essentially the art is two images broken up with vertical lines and the designs are printed, stacked on top of each other in a certain progression. Printing manually will be tough to acheive and proper tensioned and high end screens will need to be used.
www.impressionsmag.com had a pretty good article many months back that discussed the printing and art end of this effect. You should be able to request back issues from the website