Verses 1-6

NRSV
By the rivers of Babylon— there we sat down and there we wept when we remembered Zion.
On the willows there we hung up our harps.
For there our captors asked us for songs, and our tormentors asked for mirth, saying, "Sing us one of the songs of Zion!"
How could we sing the Lord's song in a foreign land?
If I forget you, O Jerusalem, let my right hand wither!
Let my tongue cling to the roof of my mouth, if I do not remember you, if I do not set Jerusalem above my highest joy.

KJV
By the rivers of Babylon, there we sat down, yea, we wept, when we remembered Zion.
We hanged our harps upon the willows in the midst thereof.
For there they that carried us away captive required of us a song; and they that wasted us required of us mirth, saying, Sing us one of the songs of Zion.
How shall we sing the Lords song in a strange land?
If I forget thee, O Jerusalem, let my right hand forget her cunning.
If I do not remember thee, let my tongue cleave to the roof of my mouth; if I prefer not Jerusalem above my chief joy.

• We know this is a later psalm because it references the destruction of Jerusalem at the hands of the Babylonians, which happened around 586 BCE. To give you some context, people think David lived around 1000 BCE or so.
• The rivers of Babylon are where they are now—i.e., not Israel.
• The psalm serves two purposes: (1) lament and (2) prayer for vengeance.
• Whenever a culture is displaced or endures a shock, it immediately goes into preservation-mode. Think of any major cultural shock and you'll know what we mean.
• What we get in these first verses is just plain sadness. The Israelites don't want to be in exile because they're farther from God's land.
  Also, if they forget Jerusalem, they don't want to write about anything because nothing else deserves it.
• The Israelites' culture is so tied up with their land—remember all that nature imagery?—so losing their land means losing much, much more.

Verses 7-9

NRSV
Remember, O Lord, against the Edomites the day of Jerusalem's fall, how they said, "Tear it down! Tear it down! Down to its foundations!"
O daughter Babylon, you devastator! Happy shall they be who pay you back what you have done to us!
Happy shall they be who take your little ones and dash them against the rock!

KJV
Remember, O Lord, the children of Edom in the day of Jerusalem; who said, Rase it, rase it, even to the foundation thereof.
O daughter of Babylon, who art to be destroyed; happy shall he be, that rewardeth thee as thou hast served us.
Happy shall he be, that taketh and dasheth thy little ones against the stones.

• Well, this got harsh pretty quickly.
• The vengeance the author hopes for is decidedly violent: he dreams that the Babylonians' children will be thrown against the rocks. Well then.
• Did you notice that the writer almost lets God off the hook for letting Jerusalem fall? All he does is ask that God remember what happened. 
• At this point, the writers of the Bible started thinking about God as more universal rather than in "your god vs. my god" terms. Before, God was one among many—the Israelites just thought he was the best. But the traumatic fall of Jerusalem made them think twice…and psalms like this usher in a new era.