There are a lot of questions on this site that ask for details of events that aren't provided in the scriptures, and I'm not sure what questionners are expecting to get other than speculation. So I'll provide some of the traditional answers, but these are all speculation.
Note that most of the rabbinical interpretations and many of the Christian interpretations also refer to Ham's blessing as preventing Noah from cursing Ham. In what follows, I will skip that part.
Rashi points out four options:
Genesis 9:22 — וירא חם אבי כנען AND HAM THE FATHER OF CANAAN SAW —
Some of our Rabbis say that Canaan saw it and told his father about
it, and on that account he is mentioned in connection with this matter
and was cursed (Genesis Rabbah 36:7).
וירא את ערות אביו AND HE SAW HIS FATHER'S NAKEDNESS — Some say that he
castrated him and some say that he sodomized him (Sanhedrin 70a).
e.g, that it could have been Caanan who did X and then told Ham, or perhaps Ham did X, where X is either castrate Noah or Sodomize him.
If castration, then the idea would be that as Noah can't have more sons, then he will curse Ham's son. The castration option was supposedly motivated by Ham not wanting to share the world with more sons, as a three way split was enough:
Genesis 9:25 — ארור כנען CURSED BE CANAAN — You have brought it about
that I cannot beget a fourth son to serve me; cursed, therefore, be
your fourth son (see Chap. 10:6) to serve under the descendants of
these elder ones upon whom the duty of serving me will devolve from
now on. Why did Ham maltreat him in this manner? He said to his
brothers, “Adam Harishon had two sons and one killed the other in
order that he might possess the whole world(Genesis Rabbah 36:7): our
father already has three sons, and he wishes to have yet another “.
Rashi Commentaries. (n.d.). (p. 33).
There are other options that "expose nakedness" is a reference to raping Noah's wife, and thus Canaan was actually the son of Noah's wife and Ham, which is why he was cursed. In this interpretation, Noah notices this only after some time and the bedcover is placed over the wife.
Of all of these rabbinical interpretations, I think castration is the most plausible in terms of fitting the text.
Luther has a beautiful interpretation, which does not assume any euphemisms for uncovering nakedness, and merely points out that in Noah's shame and humility, God grants him a revelatory vision. So Noah's curse is more of a prophecy brought on by God rather than any kind of vengenance, and the humility of the experience is what brings this prophecy on.
- Also the punishment of this wickedness is carefully set before us. Noah, looked upon by his son as a foolish, insane, and ridiculous
old man, now steps forth in the majesty of a prophet, to announce to
his son a divine revelation of future events. Truly does Paul declare
that “power is made perfect in weakness” (2 Cor 12:9); for the
certainty characterizing Noah’s utterance is proof that he was filled
with the Holy Spirit, notwithstanding that his son had mocked and
despised him as one utterly deserted by the Holy Spirit.
Luther, M. (1910). Luther on Sin and the Flood: Commentary on Genesis. (J. N. Lenker, Ed. & Trans.) (Vol. II, p. 314). Minneapolis, MN: The Luther Press.
Calvin also focuses on the curse as coming from God rather than Noah, but as he does not focus on Noah's weakness, the exegesis is more cerebral and complex:
It is strange that Noah curses his grandson and passes over in silence
Ham who committed the crime. The Jews give God’s favor as the reason
and say that God had so greatly honored Ham that the curse was shifted
to his son. But that is a foolish conjecture. I am sure that the
punishment was transferred to posterity to make its severity all the
more obvious; for God was giving clear testimony that he did not
consider the punishment of one man alone to be sufficient, and that
therefore the curse had to include his descendants and continue in
force through the ages. Meanwhile Ham himself was certainly not
exempted; God made his judgment heavier by including his son with him.
Now another question arises. Why did God single out from among Ham’s
many sons one man in particular for the blow? But here we must not
allow too much range to our curiosity. We should keep in mind, it is
not without reason that the judgments of God are called an
unfathomable abyss. It is not fitting that God, before whose tribunal
we must all finally stand, be subjected to our judgment—or rather to
our foolish temerity. God chooses as he pleases some, to make them
examples of his grace and long-suffering; he destines others for a
different purpose, to be proofs of his anger and severity. Here human
minds are blind; yet each one of us, knowing his own failure, should
learn to praise God’s justice rather than hurl himself by insane
audacity into the deep abyss. The curse of God included the whole seed
of Ham. But he singled out the Canaanites by name as cursed above all
others. We know that this judgment was from God, for it was afterwards
validated by the event. Noah was a man and did not know what was to
happen to the Canaanites; but in such obscure and hidden matters he
spoke as the Spirit directed his tongue. There is still another
difficulty. The Scripture teaches that the sins of men are punished to
the third and fourth generation; and yet [our text] seems to depict
the punishment of God’s wrath as reaching to ten generations. I
answer: Scripture does not prescribe a rule which God himself may not
transgress, as though he were bound not to punish beyond four
generations. We must see grace and punishment as combined and so
understand that, while God justly punishes our crimes, he is still
more inclined to mercy. Meanwhile, let us admit that he is free to
extend punishment as far as it seems good to him.
Haroutunian, J., & Smith, L. P. (1958). Calvin: Commentaries (p. 275). Philadelphia: Westminster Press.
Ephraim the Syrian (363-373)
Argues that Canaan saw the nakedness, told his father, and the father joked about it.
Noah cursed Canaan, saying, “Cursed be Canaan. A slave of slaves shall
he be to his brothers.” But what sin could Canaan have committed even
if he had been right behind his father when Ham observed the nakedness
of Noah? Some say that because Ham had been blessed along with those
who entered the ark and came out of it, Noah did not curse Ham
himself, even though his son, who was cursed, grieved him greatly.
Others, however, say from the fact that Scripture says, “Noah knew
everything that his youngest son had done to him,” it is clear that it
was not Ham who observed his nakedness, for Ham was the middle son and
not the youngest. For this reason they say that Canaan, the youngest,
told of the nakedness of the old man. Then Ham went out and jokingly
told his brothers. For this reason then, even though it might be
thought that Canaan was cursed unjustly in that he did what he did in
his youth, still he was cursed justly for he was not cursed in the
place of another. Noah knew that Canaan would deserve the curse in his
old age, or else he would not have been cursed in his youth.
COMMENTARY ON GENESIS 7.3.1–2.
Louth, A., & Conti, M. (Eds.). (2001). Genesis 1–11 (p. 158). Downers Grove, IL: InterVarsity Press.
Justin Martyr (100-165)
In the blessings with which Noah blesses his two sons, he also curses
his son’s son. For the prophetic Spirit would not curse that son
himself, since he had already been blessed by God, together with the
other sons of Noah. But, since the punishment of the sin was to be
transmitted down to all the posterity of the son who laughed at his
father’s nudity, he made the curse begin with the son’s son
Louth, A., & Conti, M. (Eds.). (2001). Genesis 1–11 (p. 159). Downers Grove, IL: InterVarsity Press.
I'll stop here as my reading hasn't revealed any new arguments than what have already been made.