Genesis 9:18-28

18The sons of Noah who came out of the ark were Shem, Ham and Japheth. (Ham was the father of Canaan.) 19These were the three sons of Noah, and from them came the people who were scattered over the whole earth.

20Noah, a man of the soil, proceeded^a to plant a vineyard. 21When he drank some of its wine, he became drunk and lay uncovered inside his tent. 22Ham, the father of Canaan, saw his father naked and told his two brothers outside. 23But Shem and Japheth took a garment and laid it across their shoulders; then they walked in backward and covered their father’s naked body. Their faces were turned the other way so that they would not see their father naked.

24When Noah awoke from his wine and found out what his youngest son had done to him, 25he said,

This is some very important information regarding genealogy.  We will see the lines of Ham, Shem and Japheth and the differences of personalities making very different cultural people (all people come from these three men).  Do you think you belong to your family?  You are likely a lot like some of your lineage and your culture as a whole.  

Here we see Noah become drunk, and so drunk that he passes out in his tent butt naked. There is an unpleasant, sinful implication here regarding Ham the father of Canaan.  He clearly saw his father naked.  It is implied that something may have happened in the sense that Ham mistreated his father in his drunken state (one side theologians ascribe to).  Whether Ham just looked at his father with sinful eyes (other side theologians ascribe to) or he did something worst, it's clear in Scripture that Ham sinned against God in this moment.  Shem and Japheth take a garment into cover their father while turned the other way not to see his naked body.  

When Noah woke, he found out what his son Ham had done.  This is an implication that something unpleasant was done to Noah while he was passed out, whether it was mocking his naked body or something worst, Scripture does not say exactly.  But we do know that this sin was bad enough to curse the entire line of Canaan (Ham's son's lineage).  We are unsure why God chose one of Ham's son's to curse, but his sons were Cush, Egypt, Put, and Canaan. (Gen 10:6)   Scripture doesn't say but it's possible that Noah had also seen Ham's sinful weakness in his grandson Canaan.  Again, we are unsure according to Scripture. 

Going forward, keep in mind the curse of the Canaanites.  This passage will be very important as we see this genealogy unfold.  The Canaanites will be cursed being the lowest of slaves to the brothers lineage.  Remember this is due to sin.  This is the beginnings of understanding generational sin.  And we will see later in Scripture the immorality of the Canaanites.  

Keep in mind that God looks at the heart while man looks at the outward appearance.  

Genesis 9:1-18

1Then God blessed Noah and his sons, saying to them, “Be fruitful and increase in number and fill the earth. 
2The fear and dread of you will fall on all the beasts of the earth, and on all the birds in the sky, on every creature that moves along the ground, and on all the fish in the sea; they are given into your hands. 3Everything that lives and moves about will be food for you. Just as I gave you the green plants, I now give you everything.

4“But you must not eat meat that has its lifeblood still in it. 5And for your lifeblood I will surely demand an accounting. I will demand an accounting from every animal. And from each human being, too, I will demand an accounting for the life of another human being.

7As for you, be fruitful and increase in number; multiply on the earth and increase upon it.”

God's commanded Adam and Eve to be fruitful and multiply, and here He tells Noah the same thing.  God also tells this to Abraham, as well as Jacob.  This is a command that is thread throughout God's word.  Aren't children a blessing from the Lord?  It is a direct command from God to expand His number of children and reproduce.  However, don't be discouraged if you don't have children, as Paul encourages the single person in their undivided devotion to God.  

Verse 2 says that fear and dread will fall on the animals.  Do you often wonder how in the world did Noah gather all these animals, as they are terrified of man? It seems to me according to this verse that it wasn't always this way.  It must have been a different kind of world with the animals were without fear of Noah as he gathered them into the ark.  

God now gives all of the animals of the earth to Noah and his family as food. We see some ground rules that God lays down with Noah and mankind.  They are not to eat the blood of animals or any living thing.  
God will demand an accounting for all death of man and animal.  It seems that God is saying that he will demand accounting for taking your own life or someone else's life.  The animals must not be killed with cruelty, but must be used for food or sacrifice.  God says that murder is punishable by death.  

A second time He tells Noah to be fruitful and multiply!

Genesis 8:20-22

Then Noah built an altar to the Lord and, taking some of all the clean animals and clean birds, he sacrificed burnt offerings on it. The Lord smelled the pleasing aroma and said in his heart: “Never again will I curse the ground because of humans, even though every inclination of the human heart is evil from childhood. And never again will I destroy all living creatures, as I have done.