Two clear principles are shown to us in the Bible:
Jesus teaches us to pray to the Father
When his disciples asked Jesus to teach them how to pray, this is how he instructed them, “When you pray, say: ‘Father…’” (Luke 11:1-2). In prayer, we are to address God the Father. This is to be the norm; it is the pattern Jesus gives us to follow. In giving this instruction, Jesus is not forbidding prayer directed at other persons of the Trinity, he is showing us that prayer will ordinarily be directed to God the Father.
This is a sentiment reflected by Paul. He writes to the Ephesian Christians how, “Through [Jesus] we… have access to the Father by the one Spirit” (Eph. 2:18). This is the posture of the whole Christian life, and the pattern for our praying: by the Spirit, through the Son, and to the Father.
The Spirit moves us to pray to the Father
As Paul explains the role of the Holy Spirit in the life of the believer, he emphasizes how the Spirit gives us the confidence to approach God in prayer. In fact, it is by the Spirit that we cry, “Abba, Father” (Galatians 4:6; Rom 8:15). This is not incidental. Jesus himself cried out these same words in his own prayer (Mark 14:36). The Spirit is moving Christians to address Father in the same language that God the Son uses. Prayer is a way of expressing the sonship we have through Jesus.
This is the normative shape of prayer and reflects the shape of the relationships within the Trinity: the Son lives by the Spirit to the Father. As we pray, we come in through Jesus into this eternal and happy dynamic.
Yet, the New Testament does not prohibit prayer from being directed to Jesus (or the Spirit). In fact, there are many examples of people praying directly to Jesus.
Examples like this give us a precedent for doing the same – it is good, right, and proper to pray to Jesus. (There are no examples of praying directly to the Spirit, but we can assume this too is not forbidden.)
Given the biblical precedent of praying to Jesus, and considering all that Jesus is to mean to his followers, it would be odd for a Christian never to pray to Jesus. In this sense, we should pray to him; it should be natural to cry out to him in adoration for all he has done and for help to follow in his footsteps. But we can also see that prayer should not always be directed to him. Jesus himself teaches us to pray to the Father.