"The angel said to those who were standing before him, 'Take off his filthy clothes.' Then he said to Joshua, 'See, I have taken away your sin, and I will put rich garments on you.'" NIV translation
We see here that it is God that removes the filthy rags from our old sinful bodies. There are many that want to clean themselves up a bit before they accept Christ as their savior but, as we see here, this is the work of God and not man. There is no twelve step program or anything else except the action of God in a person's life. We also see that God does not want us walking around naked but after the old is removed He puts "rich garments" on us. All of this is a work of God and a wonderful picture of grace.
"Then I said, 'Put a clean turban on his head.' So they put a clean turban on his head and clothed him, while the angel of the Lord stood by." NIV translation
The sin has been taken away and paid for by Jesus. Now, we see a changing of the mind as a new turban is given to cover the head.
This changing of the mind is an agreement with God that His ways are right (ours are not) and we want to follow His ways instead of our own. This is described as a renewing of our minds and is called repentance.
Even this is a gift of God (grace) because on our own we would not come to repentance.
"The angel of the Lord gave this charge to Joshua: 'This is what the Lord Almighty says: "If you will walk in my ways and keep my requirements, then you will govern my house and have charge of my courts, and I will give you a place among these standing here."'" NIV translation
After we are cleaned up and our minds are renewed, God has a purpose and plan for each of us (see Ephesians 2:10). We see this here as Jesus promises rewards to the high priest for his faithful service.