How should Christians pray? Who exactly do they pray to? Since Christians believe in the Trinity (God the Father, God the Son and God the Holy Spirit) can we then pray to anyone of the Trinity?
First off let me say that God sees our hearts and knows when we are calling on him even when we get the order a little skewed or we use the "wrong" words or when we just don't know exactly what to say. God knows and God hears us when we call on him.
Let's look at what Jesus taught about prayer. When asked by his disciples that he teach them how to pray he gave them what we now call The Lord's Prayer." It begins with the words, "Our Father" which means that it is directed towards God the Father.
When Jesus prayed who did he pray to? He prayed to his and our Heavenly Father. In several passages of scripture he directed his disciples to ask the Father but to do so in the name of Jesus. Not a formulaic kind of phrase but rather under the authority of Jesus we may come freely and boldly directly to the Father. (John 14:13-14; 15:16; 16:23-24, 26-27)
What about the Holy Spirit? Can we pray to him since he is also God?
There is no indication in scripture that we are to pray to the Holy Spirit but rather we are told over and over again to pray "in" in the Holy Spirit and that the Holy Spirit prays through us when we don't know what to pray. So the Holy Spirit directs prayers through us to the Heavenly Father.
So we pray to our Heavenly Father, in the name of (or under the authority of) Jesus, in the Holy Spirit. Does that mean that God does not hear us if we pray incorrectly? Or that we should follow the formula exactly?
Remember that God is not into formulas. He's into relationships. When we are in right relationship with him through faith in Christ then as we pray even if we don't get it right all the time we know that God hears us. Too often we get wrapped up in trying to follow some sort of pattern or formula when our focus is simply talking to our Heavenly Father and bearing our souls to him in prayer.
As we mature in our Christian faith we learn to prayer better, fuller prayers but we should not look down on those who are still learning to pray. They will get it in time. It's the journey and how we walk with God that matters.
So in closing, we pray to our Heavenly Father, in the name of Jesus in the Holy Spirit.