Read John 14:12-17
Each member of the Trinity has a distinct role in prayer.
The Father waits at the throne of grace to hear the prayers of us who trust His Son. The Lord Jesus Christ is our Advocate in the presence of God the Father. The Holy Spirit, on the other hand, is the Advocate in our hearts, teaching us to pray.
We can view it from another position. The Holy Spirit in us prepares the case we need to make. Christ pleads that case before the Judge. God the Father, as the Judge, hears the case.
So we pray to the Father through the Son in the power of the Holy Spirit.
Prayer is not something natural. Prayer to God is not the same as communion with our family or friends. It is on a spiritual level and goes beyond the natural and the physical.
The Son receives from the Father and reveals for our benefit what God wants us to know. But the Holy Spirit within us acts as an interpreter of spiritual truths.
Christ's unceasing intercession for us is indispensable. We need this in order to receive that which the Father has planned for us.
But just as essential is the intercession of the Spirit within us, praying for these things in our behalf and accepting from the Son what the Father desires to provide us with.
"If ye abide in me, and my words abide in you, ye shall ask what ye will, and it shall be done unto you" (John 15:7).