Somehow I managed to reach adulthood without ever being introduced to magic eye pictures. They are fantastic, in my opinion. The key is to be able to change your eye focus to a place beyond the surface of the picture. When I was a young girl, my optometrist suggested an eye exercise for me. He told me to take a string about 18" long and tie a knot in the middle. I was supposed to hold one end at my nose and the other end out in front of me. By changing my focus from the knot to the far end of the string and back again, I would exercise my eyes. Depending on where I looked, the string would take the appearance of an X or a V. The same principal is employed to view magic eye pictures. Incidentally, when I was a kid, there was a book of illusions which showed how to see a magic "floating frankfurter" between one's index fingers. (Basically your fingers are almost, but not quite, touching; you focus beyond your fingers, and you see the space between your fingers in a separate place with each eye so that the tips of each finger seem merged to form the frankfurter.) I never did quite get the hang of it as a kid, but I have figured out how to do it now. Again, that principal of changing the depth of focus is the same one for the magic eye pictures.
HERE is a site that has a weekly magic eye picture to enjoy.