Prayer, in some form or another, is a universal human constant. Everyone prays. An atheist might pray, "please let this lottery ticket be a winner." Even though the individual isn't invoking any particular god, it is still a prayer of sorts. Also, all religions consider prayer to a god or a pantheon of gods an integral part of their religious practice. Christians pray to God, who is clearly characterized by Biblical scripture. Without regard to any person's religion or lack of religion, all people pray in one form or another. It's part of being human.
Prayer in Christianity
First things first, you must approach prayer from the proper perspective. We must be in a proper relationship with God before we request anything from God. Even the first prayer a Christian prays to God must come from believing in Jesus as Savior. Also, as we relinquish our lives to Christ as our Lord, we must pray in a manner that glorifies God and seeks His will, not our will.
We must seek God's glory. Our needs should be tertiary to God's needs and the needs of others before our needs, and then our focus should always be God's glory. Matthew 6:9-13 says, "After this manner, therefore, pray ye: Our Father which art in heaven, Hallowed be thy name. Thy kingdom come, Thy will be done in earth, as it is in heaven. Give us this day our daily bread. And forgive us our debts, as we forgive our debtors. And lead us not into temptation, but deliver us from evil: For thine is the kingdom, and the power, and the glory, forever. Amen."
Focus on God's purposes before you focus on your priorities, and God's purposes will become your priorities. In other words, we should always want God's perfect will without regard to our priorities, and as we focus on His will, His will becomes our priority. There is a convergence of wills.
We must also focus our prayers on others before ourselves. Then the answers to our prayers for others bring as much or more joy than answers to prayers for ourselves. We can count it all joy when God answers the fervent prayer of a Christian for someone else in need. We should always pray for our needs last.
I know it's unpopular nowadays, but we should always seek holiness before happiness or pleasure. We should be more eager to be Christ-like than comfortable, so asking for stuff that glorifies us instead of God is inappropriate. Everything we ask for in prayer should be Biblically appropriate, glorify God, and not involve sin. In other words, don't pray a person will lose their job but instead pray that the person becomes better at their job. Praying for the betterment of the person is Biblical and imparts forgiveness and grace. If God answers yes, your prayer will bring glory to God through answered prayer.
How Should We Pray?
I was taught using the acronym ACTS as a guide following the formula presented in the Lord's Prayer. Matthew 6:9-13.
Adoration or Praise. The Book of Psalms in the Old Testament contains far more prayers of adoration than any other book in the Bible. But we also see expressions of praise found in many other books of both the Old and New Testaments. Our Lord is worthy of all praise, and we should show Him our adoration from the beginning of our prayer.
Confession. Prayer is not simply an individual matter. We all share in the sins of the body of Christ and our national sins in some way, even if we personally do not commit those sins. We have all sinned and fallen short. David recorded a prayer in Psalm 51, dealing primarily with personal sins and failures. Nehemiah (Nehemiah 1:5-7) and Daniel (Daniel 9:1-19) prayed prayers dealing with the sins of larger groups such as the nation of Israel. So, we should confess our sins and the sins of our leadership, country, and humanity.
Thanksgiving. When we pray prayers of thanksgiving, we demonstrate that we realize that our blessings come from God. Others may share in the same blessings we do (food, clean water, protection, safety, etc.) without acknowledging God as the source of those blessings. Through prayer, we recognize God in every situation and every area of life. He is our Father, our Savior, our Provider, our Protector, and our Guide. He is to receive all the honor, glory, and thanksgiving. He is the one who can grant forgiveness, mercy, grace, and peace. So, we thank God for everything always.
Supplication, Request, or Petition. God is not a vending machine, but for some people, prayer is primarily a means of getting something from God. But for the sincere believer, prayer involves so much more. We pray for the needs and appeals of others. We also look to the Lord for the spiritual and eternal blessings He provides, not only for material or physical benefits. Further, we ask for these blessings not only so that our lives will be improved but so that God will be glorified in our own lives and the lives of all God's people. Make requests of God that will praise Him, not you or us.
Prayer Conclusion
There is so much more that can be said and written about prayer – true prayer that glorifies God. But I'll end this with what prayer is not. Prayer is not by your will and to your glory. You cannot control God. If He answers yes to your prayer, it's because it was His will, not yours. God is not a vending machine. So, you don't just stick your prayer in and get exactly what you want. If God wants you to have your heart's desire, He ordained it before He created this universe. If God says no to you, he ordained His answer before He created this universe. Prayer is a means for you to develop a relationship with God, not for you to get your prayers answered to satisfy your will. Every answer to every prayer had an answer from the beginning, but we need that communication and communion with God, so prayer is an essential part of our lives. Always pray to glorify God, and you can't go wrong. And always pray in Jesus' name because Jesus is the mediator between God and us.