Ed Clowney wrote an article on prayer some time ago entitled A Biblical Theology of Prayer.  This is a great article.  You can read the pdf. from www.beginningwithmoses.org.

Here is a great quote from the article:
We dare not address the Father without awareness of the Son. To do so would be to fail to pray in the name of Jesus. Nor should we pray without recognising that the Lord is present to help us, present in the abiding reality of the Holy Spirit. To be sure, in our weakness and finitude, we may think now of the Father, now of the Son, now of the Spirit. Yet we do sense that our prayer is to the Trinity. The Spirit who makes intercession for us guides our praying, for he witnesses to the Father and to the Son.

Here, too, the Scripture gives sure guidance. Clearly prayer in the New Testament is addressed to the Father. In the teaching of Jesus, in the record of Acts, in the Epistles, Christian believers bow to the Father from whom the whole family in heaven and on earth is named (Eph. 3:14). Does this uniform practice ignore or replace prayer to the Trinity? Not at all; rather, it is in addressing the Father that we can best respond to the full revelation of the Trinity. It would be foolish (indeed, blasphemous) to imagine a kind of jealousy within the Trinity, as though the Son would feel slighted by our appeal to the Father. Indeed, such a travesty is in no way possible. We cannot turn our backs to the Son in order to address the Father. The Father will not hear such prayer. Only as we come in the name of the Son can we pray to the Father.

Prayer to the Father is not a limitation of our prayer. It does not exclude Christ, but confesses the purpose for which he gave his life. He came, not only to claim those that the Father had given him, but to bring them to the Father, losing none of them (John 17:12). The triumph of the work of the Son is to make us acceptable to the Father through him (John 16:27).

Prayer to the Father exhibits the consciousness of sonship that crowns prayer in Christ. The total submission of prayer, its utter trust, looks to Jesus Christ. He is Lord; we come to him with our burden of sin and receive forgiveness and life. Yet when Jesus receives us to himself and unites us to himself we are more than delivered from sin, more than made heirs of eternal life: we are brought into a relation with God the Father that can exist only because Jesus is the divine Son. We are made sons of God. Yes, children by the new birth, but, in a sense, more than children. In Christ there is no longer male and female: we are sons in the Son.

The lessons of prayer all hinge on this incredible reality; we bring to the Father the dedication of our new obedience (Rom. 12:1, 2); we recognise his discipline (Heb. 12:5-7); we seek his will, his plan, his kingdom. In the urgency of our helpless need, we come to him with importunity, knowing that our Father will not give us a stone for bread (Luke 11:11-13).

The prayer of sonship to the Father breathes assurance as well as dependence. We realise that the love of the heavenly Father is all our hope. Surprisingly, Paul writes, 'But God demonstrates his own love for us in this: While we were still sinners, Christ died for us' (Rom. 5:8). Since Paul was speaking of the willingness of a man to give his life for a friend, we should have expected him to write, 'But Christ demonstrates his own love . . .' Calvary displays not only the love of the Son who gave himself for us, it demonstrates the love of the Father, who gave his only Son.

All the delight of heaven itself begins in prayer as the Spirit of the Father and of the Son draws us into communion with the triune God. We pray, 'Abba, Father!' and our fellowship is with the Father and with his Son, Jesus Christ (1 John 1:3).