When we pray, does Jesus hear us? Is there a direct point of contact or is it received by all three persons of the trinity simultaneously?
There is no way to know for certain, and given that God knows your prayers before you pray them, if you will, before the foundation of the world, the direct path of your prayer is somewhat immaterial.
Those who dwell in him, indeed, must also have this knowledge as well; but in a more limited fashion since they are not God.
For the second part, the Father, Son and Holy Spirit fully indwell one another, thus aside from the aspect of incarnation, it is impossible to make such a distinction.
Short answer: My understanding is that "we pray to the Father, in the name of the Son, with the help of the Spirit."
- Passages that lead me to believe we should be praying to the Father, specifically:
[Jesus:] "when you pray, go into your inner room, close your door and pray to your Father who is in secret" (from Matthew 6:6, NASB)
"[Jesus] said to them, 'When you pray, say: "Father,..."'" (from Luke 11:2, NASB)
"[Jesus] fell on His face and prayed, saying, 'My Father,..." (from Matthew 26:39, NASB)
- Passages that lead me to believe we should pray in the name of the Son, specifically:
"[I, Jesus] appointed you that you would go and bear fruit... so that whatever you ask of the Father in My name He may give to you." (from John 15:16, NASB)
[Jesus:] "In that day you will ask in My name, and I do not say to you that I will request of the Father on your behalf; for the Father Himself loves you..." (from John 16:26-27, NASB)
- Passages that lead me to believe we should pray with the help of the Spirit:
"In the same way the Spirit also helps our weakness; for we do not know how to pray as we should, but the Spirit Himself intercedes..." (from Romans 8:26, NASB)
"With all prayer and petition pray at all times in the Spirit..." (from Ephesians 6:18, NASB)
"But you, beloved, building yourselves up on your most holy faith, praying in the Holy Spirit," (Jude 1:20, NASB)
Let's say you write a letter to the CEO of a company: one important thing you need is the address. Even if you take it there in person, you first meet the front desk manager/assistant or receptionist. The letter goes through him or her before it is handed over to the boss.
"Jesus saith unto him, I am the way, the truth, and the life: no man cometh unto the Father, but by me. " (John 14:6).
"And in that day ye shall ask me nothing. Verily, verily, I say unto you, Whatsoever ye shall ask the Father in my name, he will give it you. " (John 16:23).
Jesus is the address or the receptionist, the path.
The Holy Spirit is God's active force that we pray for, for him to use to empower us and direct us to carry out his works.
1 Samuel 10:6 "The Spirit of the LORD will come upon you in power, and you will prophesy with them; and you will be changed into a different person."
Well don't try to imagine that there is Complicated Prayer System or algorithm in heaven.
Just hold this very word of Jesus:
"And I say unto you, Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you." (KJV) Luke 11:9
The prayer path is simple one: ask and you'll receive the answer.
Please read Luke 11:1-13 so we may understand what was exactly Jesus trying to teach us regarding prayer. Let us beware so that our intelligent didn't hinder us from understanding God.
At that time Jesus answered and said, I thank thee, O Father, Lord of heaven and earth, because thou hast hid these things from the wise and prudent, and hast revealed them unto babes. (KJV) Matthew 11:25
In response of @waxeagle 's demand:
First, let us see what's Jesus intention:
And he said unto them, I must preach the kingdom of God to other cities also: for therefore am I sent. (KJV) Luke 4:43
The possible question arises in the people's mind is: What's the difference between this kingdom of God with all the world's kingdom so that it's important to be preached?
Jesus provide the answer through Lord's Prayer as we already know it:
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. (KJV) Matthew 6:9-10
Unlike all the world's kingdom, God, the King himself is our Father. The hassles (path, system, rules, algorithm, laws) we going through to speak (pray) to the King is present no more. I believe everyone here can easily talk to their own father.
The law and the prophets were until John: since that time the kingdom of God is preached, and every man presseth into it. (KJV) Luke 16:16
Examples some of the hassles before the time the kingdom of God is preached:
- Saul need to use Samuel as mediator to pray to God. (1 Samuel 15:16)
- Just to ask for forgiveness the children of Israel must perform certain ritual, moreover only High Priest permitted to talk to God (pray). Read Leviticus it has a lot of old rules related to prayer.
In the evening in Galilee.
Disciples: Rabbi, how's the rules (path, system, algorithm, laws) so that our prayer reach God (King)?
Jesus: It's simple, there's no rule, just go and talk to Him. He's our Father after all.
I hope it helps. God bless you.