"God plays the symphony of our salvation in three movements," say Philip Graham Ryken and Michael LeFabvre in Our Triune God. Each of these movements is associated with and facilitated by a different Person of the Trinity.
The Father: Salvation originated with the Father. Ephesians 1:3-6 tells how the Father chose us before the foundation of the world, and predetermined our adoption as this children through Jesus Christ. The Father is the administrator of salvation, and he oversees the process from beginning to end.
The Son: Salvation is brought to fruition in the Son. Everything the Father does for our salvation, he does through Christ. The work of the Son means redemption, adoption to the Father, reconciliation, sanctification, and glorification (Ephesians 1:7-12). It operates horizontally as well as vertically, and it is for Jew and Gentile alike. It is through the Son that we achieve salvation and come into full relationship with the triune God.
The Spirit: Salvation is communicated by the Holy Spirit. The Spirit changes us from the inside out, preforming the gracious act of regeneration. With this comes the gift of faith and the spiritual ability to believe in the Resurrection. Through the Holy Spirit, our salvation becomes a present reality, applicable to our lives in our own specific context. It is the work of the Holy Spirit in our lives that serves as a seal, establishing us as children of God (Ephesians 1:13-14).
Excerpt modified from of Our Triune God.