Daniel 9:1 & 2

"In the first year of Darius son of Xerxes (a Mede by descent), who was made ruler over the Babylonian kingdom - in the first year of his reign, I, Daniel, understood from the Scriptures, according to the word of the Lord given to Jeremiah the prophet, that the desolation of Jerusalem would last seventy years." NIV translation

Daniel saw another king come to power and so he studied the Scriptures of Jeremiah and found that the captivity in Babylon would last for seventy years. This is a reminder to us that we need to look at the world events of today and study our Bible to understand what is going on. 

Daniel 9:3

"So I turned to the Lord God and pleaded with him in prayer and petition, in fasting, and in sackcloth and ashes." NIV translation

He knew that the only way that he could influence the events of his time was through prayer and so he turned to God. In this verse, we see a pattern for effective prayer. First, we see that he did not go to God with a bunch of babbling but instead took his request to the throne of God. We also see that he prepared for prayer in the fact that he fasted and put on sackcloth and ashes. The sackcloth and ashes were signs of repentance and coming to God in humility.

Daniel 9:4 - 6

"I prayed to the Lord my God and confessed: 'O Lord, the great and awesome God, who keeps his covenant of love with all who love him and obey his commands, we have sinned and done wrong. We have rebelled; we have turned away from your commands and laws. We have not listened to your servants the prophets, who spoke in your name to our kings, our princes and our fathers, and to all the people of the land.'" NIV translation

Daniel's prayer begins with confession of the fact that he and all of Israel were sinners. He, then, gets specific with their sins of disobeying the commands of God and ignoring the warnings delivered by His prophets.

A big part of effective prayer is going to God in humility by admitting that we are sinners. Although we are not under the Mosaic Law, we still disobey the prompting of the Spirit of God and so sin against Him every day.