The story with which the novel opens is one which Stephen's father told him, as is explained in the second paragraph. The story should then be read in the voice of a father speaking to his son: the "moocow" is about to meet a little boy, "baby tuckoo," who is Stephen himself. Stephen makes this explicit in the third paragraph of the novel, when he states, "he was baby tuckoo."

The disjointed nature of this opening chapter is intended to represent the slightly confused and fragmented way in which a young child might perceive the world. The opening story, told by Stephen's father to his son, is told in the manner of a parent addressing his child and including the child and other familiar objects in the story. Later we see Stephen's recollections of his father having had a hairy face, and looking at Stephen "through a glass"—meaning, presumably, that he wore spectacles through which he looked at his son.

Yes - Stephen is the moocow. In the first section of the first chapter, we get the first glimpse of Stephen's observation. The narrator says "he was baby tuckoo" meaning that his father always told him that he was baby tuckoo. This is a very basic illustration of what Stephen remembers as a little boy. Think of your first memories and how disjointed they are and you can kind of get the drift. At the end of the section on the second page of the novel, Stephen is hiding under the table because he apparently told his neighbor Eileen (who is Protestant - Stephen is Catholic) that he would marry her when he grew up. As such, he is told that he will apologize or else an eagle will come and pull out his eyes. These are all first memories of Stephen's.