This is it, the whole thing, selected for you with care and love after many years of Ulysses reading, teaching, and writing. Memorize only a few of these sentences from Joyce's novel, and you will be ready for this year's festivities. (See my earlier Bloomsday column  for details on the June 16 holiday.)
This column will feature must-have sentences from the first half of the book; hold on while I prepare column two, with sentences from the second half.
Page numbers are from the Gabler edition. 
1. ) Stephen Dedalus, displeased and sleepy, leaned his arms on the top of the staircase and looked coldly at the shaking gurgling face that blessed him, equine in its length, and at the light untonsured hair, grained and hued like pale oak.
From page one (well,page 3 in Gabler), our first view of - our first entry into the thoughts of - displeased Stephen, who, along with Bloomsday's hero, Leopold Bloom, will dominate Joyce's novel. He's glaring at his tower-mate, Buck Mulligan, who's been amusing himself with a nasty parody of the Catholic mass. Stephen will spend the entire book in a bad mood, from which, at the very end, Bloom will somewhat rescue him. Learn this sentence because it is echt-Joyce: long, lovely, with internal rhyme (case/face), assonance (displeased, sleepy, leaned), odd, beautiful, retro words (untonsured), and unabashed lush romantic simile (grained and hued like pale oak).
2.) - You behold in me, Stephen said with grim displeasure, a horrible example of free thought.
Page 17. Grim, cold, displeased Stephen talks to his other tower-mate, a British guy. Stephen's exit from the Catholic church (he once considered being a priest), hasn't exactly opened up a glorious new world of liberation for him. He's consumed by guilt for having refused to pray with his dying mother, and is lonely and unloved.
3.) - I fear those big words, Stephen said, which make us so unhappy.
Page 26. Stephen converses with a third person, the pompous schoolmaster who employs him as a teacher. Here we begin to see the affinity that will express itself at the end of the novel between Bloom and Dedalus. Both abhor the big vague emotive concepts (nation, justice) that people may invoke to rationalize atrocious behavior.
4.) Remember your epiphanies written on green oval leaves, deeply deep, copies to be sent if you died to all the great libraries of the world, including Alexandria?
Page 34. Okay, now Stephen's talking to himself; this is Joycean stream of consciousness, and Dedalus is laughing bitterly at his naive grandiose literary ambitions. He's a blocked writer - one of many sources of his current melancholia.
5.) Put us all into it, damn its soul.
Page 111. A newspaper man talks to Dedalus and asks him, basically, to write Ulysses. Write a great novel, and put us all into it. Exactly what James Joyce did.
6.) Could never like it again after Rudy.
Page 137. Now we're in Leopold Bloom's stream of consciousness. His son, Rudy, died at eleven days old, eleven years ago. Since that, the act of sex with his wife has been caught up for Bloom with death, and he doesn't like it anymore.
7.) Joy: I ate it: joy.
Page 144. Bloom spends a good deal of the day remembering his early years of passion with his wife Molly. Here he recalls their first kiss, when she transferred a bit of cake still in her mouth to his mouth.
8.) A man of genius makes no mistakes.
Page 156. This is Stephen in conversation with fellow writers and scholars in the National Library. He's defending Shakespeare, but the remark really points to Stephen's self-destructive arrogance.
9.) Word known to all men.
Page 161. Still in Stephen's thoughts. He's referring to the word love; and he will repeat this formulation - word known to all men - frequently as the book proceeds.
10.) He bore no hate.
Page 234. Bloom's thoughts as he listens to music in a hotel go to the cruelties committed against him (his wife is openly adulterous; he was not long before this scene viciously attacked by an anti-Semite) and his lack of hatred toward the perpetrators.
11.) Still he's the best of that lot.
Page 369. Bloom, who vaguely knows Stephen through his friendship with Stephen's father, Simon Dedalus, has been watching as grim, displeased, guilt-ridden, self-hating Dedalus spends the evening getting drunk and practically asking to get beaten up.
Bloom recognizes Stephen's exceptionality, senses his crisis, and is worried about him.