Prayer is a wonderful privilege enjoyed by those who are children of God. Through prayer we receive mercy and grace to help in time of need (Hebrews 4:14-16). Through prayer we find peace that guards our hearts and minds (Philippians 4:6-7). This assumes, of course, that our prayers will be heard. Some prayers are not acceptable to God (Proverbs 28:9). Some prayers are not heard by God (Isaiah 59:1-2, James 5:16).
Consider Jesus' teaching concerning prayer in Matthew 6:5-15. Jesus taught how we are not to pray. We are not to pray in order to be seen by men (Matthew 6:5). Instead, we are to go into our closet (private chamber) to pray. Jesus was not condemning all public prayer (consider Paul's prayer recorded in Acts 27:35). But he was condemning the motive of those who prayed in order to be seen by men.
We are not to pray in order to be heard of men (Matthew 6:7). Jesus criticized the use of vain repetitions. Jesus was not criticizing all repetition. Consider Jesus' own prayer recorded in Matthew 26:36-44, where he prayed a third time, saying the same words. But Jesus was condemning the use of empty repetition, void of any meaning.
Jesus taught our prayers are to be an expression of adoration to God. Notice the phrase "Our Father, which art in heaven, hallowed be thy name." Vine's Expository Dictionary of New Testament Words describes hallowed as "the opposite of common." It is unacceptable to address God in prayer in a common manner as we would another person.
Our prayers to God are to include a confession of our faults. Notice Jesus' words, "Forgive us our debts." A person who fails to recognize his sin and thus refuses to repent of his sin will not have his prayer heard by God. Also, in order to be forgiven, we must first display an attitude of forgiveness toward others (Matthew 6:14-15).
Our prayers are to include expression of our thanksgiving to God. Although this is not specifically mentioned in Matthew 6, consider Philippians 4:6 along with I Thessalonians 5:17-18 and I Timothy 2:1.
Our prayers are to include our supplications, or requests, to God. These supplications include the past (forgiveness of sins), the present (give us this day our daily bread), and the future (lead us not into temptation).