Main point summary
The only correct response one should have when exposed to the glorious character of God should be worship. Paul exhorts us, in light of seeing the mysterious glories of God (Rom 11), to present our physical selves to God in this life as a form of sacrificial worship. Romans 12 is about worshiping in Response to God's actions.
z I appeal to you therefore, brothers, 1 by the mercies of God, a to present your bodies b as a living sacrifice,
In light of what I just said about God's character and mysterious glory, I exhort you, because of God's mercy, to present your physical body to the Lord as a form of sacrifice,
holy and acceptable to God,
in a way that is holy and acceptable to Him.
which is your spiritual worship. 2
This sacrifice, similar to the reason for sacrifice of animals in the OT, is your reasonable service to God (in light of God's glory). (See Psalm 51: 16-19)
c Do not be conformed to this world, 1
Practice this spiritual worship with your physical body by not allowing your mind to be molded into wanting the sinful passions of this evil age,
but be transformed by d the renewal of your mind,
but by cultivating the renewal of your mind unto transformation of desires,
that by testing you may e discern what is the will of God,
in order to be able to test every one of your desires to determine whether it is the will of God or not,
what is good and acceptable and perfect. 2
which is a good will, the only acceptable will, and a perfect will.
The goal of transformation and sacrifice is worship. Do not let your sacrifice and transformation be an end in itself. The end goal must be Worship or sacrifice and transformation is pointless.
Worship is the logical response that happens after contemplating "the depths of the riches and wisdom and knowledge of God". If worship is not the overflow of your heart after thinking of the glorious character and actions of God, we are not seeing Him correctly.
Romans 12:2 is the manner in which we are supposed to sacrifice our bodies as worship. Paul is explaining to us how to do what God just commanded us to do in verse 1
How does one go about renewing his mind? If one is transformed by renewing the mind, what is the best way to renew your mind? A: 2 Cor 3:18. We are renewed and transformed when we "behold the glory of the Lord". As we read the Bible and see God's glory in His character, his love, his grace, and his justice, we are transformed more and more into His image.
The whole purpose of transformation of the mind is to gain the ability to determine what the will of God is in any given circumstance or desire. A transformed person should be able to look at a situation and test it by asking, "Does this align with what God calls me to? Does this desire coincide with the desires that produce a sacrificial and worship-filled heart? If not kill it! Do not be conformed to that desire. Do not let that desire linger. Do not let something that is not the will of God remain in you. Kill it.
Why does on need to know the will of God? What benefit is it to know God's will? A: if we are to present our bodies to God as a holy and acceptable sacrifice, we must be able to determine what God sees as holy and acceptable. If we can't look at a situation and determine what the holy and acceptable course of action is, then we will be unable to worship God in that situation. You cannot worship God if you do not know his will.