Tea is very much a staple in Ulysses. In the first episode, in Martello Tower, Stephen Dedalus, Buck Mulligan, and Haines are having breakfast, which includes tea. The anecdote Mulligan tells is a tale that is often retold by readers of Ulysses. The "Mary Ann" referred to is a character in an anonymously Irish bawdy song.

"Buck Mulligan, hewing thick slices from the loaf, said in an old
woman's wheedling voice:

-- When I makes tea I makes tea, as old mother Grogan said. And
when I makes water I makes water.

-- By Jove, it is tea, Haines said.
Buck Mulligan went on hewing and wheedling:

-- SO I DO, MRS CAHILL, says she. BEGOB, MA'AM, says Mrs Cahill,
GOD SEND YOU DON'T MAKE THEM IN THE ONE POT.

He lunged towards his messmates in turn a thick slice of bread,
impaled on his knife.

-- That's folk, he said very earnestly, for your book, Haines. Five
lines of text and ten pages of notes about the folk and the fishgods
of Dundrum. Printed by the weird sisters in the year of the big
wind.

He turned to Stephen and asked in a fine puzzled voice, lifting his
brows:

-- Can you recall, brother, is mother Grogan's tea and water pot
spoken of in the Mabinogion or is it in the Upanishads?

-- I doubt it, said Stephen gravely.

-- Do you now? Buck Mulligan said in the same tone. Your reasons,
pray?

-- I fancy, Stephen said as he ate, it did not exist in or out of the
Mabinogion. Mother Grogan was, one imagines, a kinswoman of
Mary Ann.

Buck Mulligan's face smiled with delight.

-- Charming! he said in a finical sweet voice, showing his whiteteeth and blinking his eyes pleasantly. Do you think she was? Quite charming!

Then, suddenly overclouding all his features, he growled in a hoarsened rasping voice as he hewed again vigorously at the loaf:

-- FOR OLD MARY ANN SHE DOESN'T CARE A DAMN. BUT,
HISING UP HER PETTICOATS ..."

This blog entry discusses the "cracked lookingglass" as the symbol of Irish art. The text is from the Telemachus episode (first episode). The three textual passages are explicated by Frank Delaney, a Joyce scholar, and presented as mini-lecture audio clips. Before beginning, there is a story told by Joyce as presented in Richard Ellmann's, Four Dubliners, which is a precursor to the "cracked lookingglass" in Ulysses.

The story: "an old Blasket Islander lived on his island from birth and knew nothing about the mainland or its ways. But on one occasion he did venture over and in a bazaar found a small mirror, something he had never seen in his life. He bought it, fondled it, gazed at it, and as he rowed back to the Blaskets he took it out of his pocket, stared at it some more, and murmured, "Oh Papa! Papa!" He jealously guarded the precious object from his wife's eye, but she observed he was hiding something and became suspicious. One hot day, when both were at work in the fields, he hung his jacket on a hedge. She saw her chance, rushed to it, and extracted from a pocket the object her husband had kept so secret. But when she looked in the mirror, she cried, "Ach, it's nothing but an old woman!" and angrily threw it down so that it broke against a stone" (69).

Ellmann claims that Joyce interpreted the story to mean, "that a mirror held up to nature will reflect the holder's consciousness as much as what is reflected."

First textual passage and explication:

Laughing again, he brought the mirror away from Stephen's peering

eyes.
-- The rage of Caliban at not seeing his face in a mirror, he said. If
Wilde were only alive to see you!

Drawing back and pointing, Stephen said with bitterness:

-- It is a symbol of Irish art. The cracked looking-glass of a servant.

http://blog.frankdelaney.com/2010/09/re-joyce-episode-11-a-cracked-looking-glass.html

Second textual passage and explication:

Buck Mulligan suddenly linked his arm in Stephen's and walked
with him round the tower, his razor and mirror clacking in the
pocket where he had thrust them.

-- It's not fair to tease you like that, Kinch, is it? he said kindly. God
knows you have more spirit than any of them.

Parried again. He fears the lancet of my art as I fear that of his. The
cold steelpen.

-- Cracked lookingglass of a servant! Tell that to the oxy chap
downstairs and touch him for a guinea. He's stinking with money
and thinks you're not a gentleman. His old fellow made his tin by
selling jalap to Zulus or some bloody swindle or other.

http://blog.frankdelaney.com/2010/09/re-joyce-episode-12-the-schmoozing-buck.html

Third textual passage and explication

God, Kinch, if you and I could only work together we might do something for the island. Hellenise it.

http://blog.frankdelaney.com/2010/09/re-joyce-episode-13-is-it-all-greek-to-you.html