The Greek meaning of the word, renewing, as found in Romans 12:2 means to renovate. Merriam-Webster defines renovate thusly: to restore to a former better state.
Surely, most are aware of the fall of man as recorded in the 3rd chapter of Genesis in the Holy Bible. With further reading, we come to understand that through the disobedience of man[kind], sin entered into the world (Romans 5:12) and with it came its wages, which is death (Romans 6:23).
I submit unto you that the mind of man, prior to the fall through disobedience, was like that of the mind of God. For we read, in Genesis 1:27, that man was created in the image and likeness of God and I am convinced that this included the mind of man as well. So when man[kind] sinned and communion with God was broken, the mind of man suffered a fall as well. Therefore, when we are born again (through spiritual birth), our minds are also in need of restoration. Referring to the above definition, we are to renovate our minds, or restore them to a former better state (the state prior to the fall). We must also understand that this renewal is an ongoing process as implied by the 'ing' suffix at the end of the word as recorded in Romans 12:2. We must refrain from becoming weary with the process, understanding that it is an ongoing one.
Understanding and accepting this, the question then becomes, how do we renew our minds so that we are not conformed to the world? One way, and a great place to start, is being mindful of what we think. We must be intentional about our thinking. Paul, in his letter to the brethren at Philippi, encouraged them (and us) to think on things that are true, just, pure, lovely, and of good report (Philippians 4:8).
This, in my experience, is a great place to begin the process of renewing your mind. I encourage you to start the transformation process today!
*All scriptural references are from the King James Version unless otherwise noted.