Salvation is the "saving" of a sinner from the righteous judgment of God. When someone appeals to God and seeks forgiveness in Jesus, his sins are forgiven. He is cleansed. His relationship with God is restored, and he is made a new creature (2 Cor. 5:17). All of this is the work of God and not of man. Salvation is a free gift (Rom. 6:23).
We are saved from damnation. When anyone sins, and we all have (Rom. 3:23, 6:23), he deserves eternal separation from God (Isaiah 59:2). Yet, because of His love and mercy, God became a man (John 1:1, 14) and bore the sins of the world in His body on the cross (1 Pet. 2:24, 1 John 2:2). We are forgiven when we realize that there is nothing we can do to earn the favor of God and we put our trust in what Jesus did for us on the cross (Eph. 2:8-9, 1 Cor. 15:1-4). Only God saves. The only thing we bring to the cross is our sin.
Both God the Father (Isaiah 14:21) and Jesus (John 4:42) are called Savior, that is, deliverer from sin. Remember, it was the Father who sent the Son (1 John 4:10) to be the Savior.