The primary thing this doctrine reveals to us is that God is not a static reality but a dynamic one. God is relationship, God is love. The Father is unbegottten, the Son is begotten, and the Holy Spirit Proceeds from the Father and, or through, the Son.
Persons are who they are by virtue of relationship to each other.
So we teach the Father is wholly in the Son and Spirit, the Son wholly in the Father and Spirit, and the Spirit, wholly in the Father and the Son. From a historical perspective, we live now in what we call the Age of the Spirit, God's presence of love, the love between the Father and the Son that existed from eternity. When we pray, we pray to the entire God, no matter which person we specify in our prayer. Although there is not an appropriateness of which to pray to, I find my prayers of thanks and praise naturally lift to the Father and Son, and my petitions for strength and healing rise to the Spirit.