I've been experiencing this kind of prayer for years now, and I have been struggling in my head to understand it. But as I continue to grow in God it's becoming clearer and clearer. I actually tried explaining it in my first writeup on prayer years ago, but now I feel I have more understanding. Things get clearer and clearer, and you get more understanding as you continue to walk with God.
"No longer I who lives, but Christ" (Gal 2:20).
That is the testimony of the Christian life. It is all about Christ living; Christ expressing the nature of God in you, Christ working out righteousness in you, Christ doing the works of the Father through you (going about the Father's business), and Christ talking to the Father through you. Yes, the Christian prayer life is Christ (the Son) having a conversation with the Father through you.
Your prayer life shouldn't be about you; what you want, what you desire, what you feel, what you think you should tell God. You died, yes that is the reality. The moment you came into Christ you died, and it is no longer you living but Christ. This means it should not be you praying but Christ; be still and let Christ in you discuss with the Father. This is why it is important to know the indwelling Christ.
If you are still enough, and if you are more conversant with the Christ in you, you should be able to perceive his desire and the things he wants to pour out to the Father. If you have apprehended that go ahead and express the Son to the Father, let him pour out himself to the Father. As you continue to express the Son, pouring him out to the Father you are learning more about the Son, and at the same time you are looking to hear the Father's response.
Off course the Father will speak back, for this is the Son in whom He is well please trying to have a conversation with Him. One of the reason Christians don't hear God speaking back to them when they pray is because it is their flesh praying and not the Son. The flesh is filthy and an enemy to God, so God would prefer not to join him in a conversation. But if it is the Son speaking He is delighted to engage him in a conversation.
So you listen to the Father's response, and surely He would respond. He would speak back to you by the Spirit, then the Son would also respond by the Spirit, and you find yourself caught up in the conversation of the Godhead – a conversation that greatly concerns you, because the Son speaking here is the you that is Christ. It is the indwelling Christ, the part of you that is utterly Christ, and his desire is to find expression through your physical body.
He wants to break out into manifesting the fullness of God through that flesh of yours, so he is communing with the Father about how to bring that into reality. You are simply to listen to the conversation of the Godhead, learn what God is doing in you at that moment, and align yourself with it – this way you will grow speedily in God. After the prayer you can sit with the Holy Spirit to help you interprete and explain what was being discussed, and tell you want to do about it, or how to align yourself to it.
Well, this kind be difficult for a new believer, but as you grow and know the indwelling Christ you should be able to enter into this kind of prayer and be caught up in the Godhead.