The principal Scripture on prayer is Philippians 4:6-7:
"Be not anxious for anything, but by prayer and supplication, with thanksgiving, make your requests known to God, and the peace that passes all understanding will keep your hearts and mind in Christ Jesus."
Prayer is just that. Letting God know what your needs are. Because God is sovereign and not a vending machine to give us everything we want, when we want, He has not promised anything that is not His will. His ways are not our ways. The immediate result of making your request known to God is the peace and assurance that He has heard your prayer and He will act according to His sovereign will.
We can't demand things of God. He is not controlled by us. Prayer is not some kind of force to twist God's arm up His back to give us what we want, now! Daniel prayed and had to wait for three weeks, and then the angel came to him and said that he was delayed because of a battle in heaven, and his visit to Daniel was just to tell him that God had heard his prayer! The angel did not say exactly when God was going to answer it. Actually it wasn't until much later when Cyrus allowed Ezra to go back and start rebuilding Jerusalem.
Most times, we pray and leave our request on God's desk for Him to consider our request and do according to His will and purpose and in his own time. The Scripture says that through faith and patience we inherit the promises. That means that we might have to wait on God for Him to work things out.
Charles Spurgeon told the story of a faithful man of God who had three sons who were not converted and had no interest in the things of God at all. After 45 years in the faith, at the point of death he lost his faith and suffered much uncertainty and fear as he died. As the sons were carrying his coffin out of the church after the funeral, one said to the others, "Our father was a faithful believer for 45 years, and he had a very difficult death. But we have never had any interest in God, so what kind of a death will we have?" As a result all three received Christ as Saviour. The father had prayed for his sons all their lives and never saw them come to Christ in his lifetime, but God answered His prayer at the best time and in the most effective way, even though it was not in the father's lifetime. There is a good lesson for us in this when we have prayed and are waiting on God for His answer.
We don't need to get anyone else either on earth of heaven to pray for us to the Father. The Scripture says, "Let us come boldly to God's throne of grace to find mercy and grace to help in our time of need."
