It is difficult to explain just one short verse, especially considering that it is a rather significant clause in a much longer sentence. But still, this verse is full of richness that is not too difficult to understand.
whom he poured out on us richly through Jesus Christ our Saviour,Titus 3:6
The entire Trinity is in this verse. The “whom” is the Holy Spirit (see the end of Tit 1:5), the “he” is God the Father, and then obviously Jesus is named at the end.
This verse means that God the Father poured the Holy Spirit out on us through Jesus Christ who is our Saviour.
This still describes how “God saved us” from verse 5, affirming that the Holy Spirit is given to believers at the moment of salvation. The Holy Spirit is given to believers as an act of God Himself, not, as verse 5 already suggested, an act by us. When we were saved by Jesus, the Father gave us His Holy Spirit.
The Father did so lavishly, ensuring that we are in no ways lacking in any of the saving graces. We are therefore fully assured of being completely saved by God’s acts in Titus 3:5, and can confidently know that Titus 3:6 is true of us.
When God saved us, He gave us His Holy Spirit completely. Jesus was God’s agent of this great gift to us..