How are we saved? First God tells us how we are not saved.
"Not by works of righteousness which we have done..."
Then - how we are:
"...but according to His mercy He saved us by the washing of regeneration, and renewing of the Holy Ghost; which He shed on us abundantly through Jesus Christ our Saviour;" Titus 3:5,6
What I love most about this is how all three members of the Triune God are busy at work on our souls: the Father as He drops His mercy and pours His abundance; the Holy Spirit as He scrubs away, regenerating and renewing; Jesus the Savior who accomplishes all through the cleansing power of His precious lifeblood that washes us as nothing else can.
An analogy comes to mind at the phrase washing of regeneraion and renewing. It is reminiscent of the lilies of the field spoken by Jesus.
Under the dead of winter the bulbs lie in their earthy tombs. Like the Holy Spirit the spring rains come and wash across the fields renewing the land. The sleeping bulbs awaken to new life. Once dormant and unseen they shoot forth beauty in living color: greens of stem and leaf: the golds and crimson of flower. Regeneration has taken place.
Of course most obvious of all is that it is God Himself who, according to His mercy and grace, does the regenerating, renewing, and cleansing. Our part is mostly to believe and submit to the quickening power of His awesome love.
"Therefore if any man be in Christ, he is a new creature: old things are passed away; behold, all things are become new."II Corinthians 5:17