Put on the new self (the new man), which is being renewed in knowledge after the image of its creator.
1) Who is the Creator referred to?
In context you'd think it was Christ, who is the Creator Image of God (Col 1:15-17)
2) What gets renewed?
The "new self" gets renewed. It's not simply that we are renewed by getting a new self. And it's not simply that we are given a new self. We are given a new self and the new self is renewed.
3) How does renewal happen?
Knowledge. Note all the knowledge language of the letter. This is just from chapter 1:
"heard... word of truth... gospel... learned... understood... all its truth... knowledge... spiritual wisdom... understanding... increasing in knowledge... make the word of God fully known... Him we proclaim... teaching everyone with all wisdom."
We desperately and continually need gospel knowledge to be renewed.
4) What does our Creator look like (given that we're supposed to look like Him)?
He is compassionate, kind, humble, meek, patient, forbearing, forgiving - in a word: He is love (v12-14). We know that these character-traits originally belong to the Lord because a) it says "Forgive as the Lord forgave you" and b) these virtues are outlined in the context of our becoming like Him.
So we don't become forgiving, humble and meek because God will hold us to account and He's big and powerful. We are forgiving, humble and meek because He is forgiving, humble and meek. And He has demonstrated it at the cross.
Therefore as we appreciate and know the goodness of this good news our new selves are being renewed to look like Christ - the compassionate and humble God.
Surprised by any of those answers?