Part 1: The Telemachiad, and "Calypso"
By the end of "Calypso," our two main characters have been introduced, and we have been given a sense of some of the main conflicts that will drive the novel. In The Telemachiad, we get a picture of Stephen as he has matured since the end of Portrait of the Artist as a Young Man. We learn that Stephen's mother died and that he is wracked with guilt over her death. In "Proteus" we also get our first really daring stylistic chapter, and begin to get a sense of the intense stream-of-consciousness and stylistic play that will come to dominate the book. "Calypso" is our first peek into the mind of Leopold Bloom. We also get a feeling for the Blooms' troubled marriage, which will come to underlie much of the book's plot.
Part 2: The Wanderings of Ulysses, in particular that Molly is going to sleep with Boylan
Along one plot line (that of Molly's adultery), the main conflict in the novel is that Bloom knows that Molly is going to sleep with Boylan before the day is out. Along another, say, Stephen's, the main conflict is that ever since the death of his mother he has been isolated from the world. Stephen needs a way to get back into the human fold. There are a number of different conflicts that arise in The Wanderings of Ulysses as Bloom confronts death at Dignam's funeral, Stephen presents his Hamlet argument, and Bloom speaks out against prejudice and shortsighted Irish nationalism. In terms of a classic plot, the main conflict is Molly's affair, but realize that much of the conflict is in the realm of ideas rather than of events themselves. The conflicts are between moderation and extremism, between religious orthodoxy and nihilism, between independence and communal feeling, between subjugation to English oppression and narrow-minded Irish nationalism, between happiness and despair.
Part 2 The Wanderings of Ulysses, in particular the fact that Bloom is going to let Molly sleep with Boylan
Along that main plot line, the complication begins to develop when we realize that Bloom has no real intention of stopping Molly from sleeping with Boylan. His passivity can be maddening, and we are forced to alter our sense of the conflict. Rather than wondering how Bloom is going to prevent the thing from happening, we have to start wondering how he is going to come to terms with it. As we noted in the "Conflict" above, there are a number of other conflicts at play in the novel, and on that level it's hard to separate those conflicts from their complication. In terms of the ideas that the book struggles with, it's really just one complication after another.
The action reaches a peak in 'Circe' when Stephen has a vision of his dead mother, knocks over Bella Cohen's chandelier with his ashplant (cane) and screams Non Serviam before running out of the brothel and getting in a fight with an English constable. In terms of our understanding of the characters, "Circe" is also a climax because we approach something like full disclosure. Their subconscious thoughts seem more liberated than they are anywhere else in the novel. In the long dreamscapes that make up "Circe," we see into Leopold Bloom's most base neuroses and his most absurd vanities. On another level, it's here that the subconscious of the book itself is let loose – all the things that were percolating between the lines of earlier chapters but could not be said are here given voice.
"Eumaeus" and "Ithaca"
There is still a great deal of unresolved conflict after "Circe." Namely, we still don't know what Leopold Bloom is going to do about his wife's affair, if anything. We also don't know whether or not Stephen and Leopold will get along as well as we would like them to (they don't). Through much of the novel, we have been made to anticipate a sort of reunion between the two in which Bloom fills the role of surrogate father for Stephen and Stephen fills the role of surrogate son for Bloom. Now that they've actually met, we have to wait and see how things play out.
"Ithaca" is, to many readers, the most satisfying episode in the entire book. Stephen and Bloom have been united, and it is here that they begin to get along and have a long discussion in Bloom's kitchen before he shows Stephen out. It is after 2am and for both of them, it is clear that the action of their day has passed and that things are now winding down.
Bloom's day concludes at the end of "Ithaca," when he kisses his wife Molly on the butt and nods off to bed. But throughout the book we have constantly been re-evaluating Bloom, looking at his situation in a number of different lights. Molly's perspective has been missing from the rest of the book, and here we get it in full force. New tension arises as we wait to see what her final judgment on Bloom will be. Will she affirm her love for her husband or deny it?