God is calling us to make a practical presentation of ourselves to Him: "Here I am, God! I'm yours, totally and completely." This must be our lifestyle. Being a "living sacrifice" is tough, because we tend to want to squirm off the altar. But when your body is yielded to God, it is a base of operations for the Holy Spirit to work. That's why the Bible calls our bodies the temple of the Holy Spirit.
The Bible is full of wonderful examples of bodies yielded over to God. Sarah's barren womb was yielded to God, and she gave birth to the son of promise, Isaac. Moses told the Lord he was "slow of speech," but he yielded his voice to God and it became a powerful instrument, to utter the law to the nation. The shepherd hands of David vanquished the giant. Paul's feet carried him to the uttermost parts of the world to spread the Gospel.
"Reasonable service" means it must be a rational choice. That makes sense if you think of all God has given to you--His salvation, His peace, His mercy. You should want to commit your life to God because God has committed to you all the resources for life and godliness.
Verse 2 talks about transformation, changing the way we think about the values around us. It says, "Don't be conformed to this world." God is calling you to non-conformity. I love the way the Phillips translation puts it: "Don't let the world squeeze you into its own mold." One of the greatest fears people have is to be rejected by "the group," their peers…to be somehow different. That's why even some Christians conform to what the world thinks and how it behaves.
We will conform to one of two value systems--to that of God and His Word, or to that of this world. One of those two molds will shape us. But our thinking is to be renewed. We are to love the Lord our God with all our heart, mind, soul, and strength.
The point is, God wants to touch the world through you. So you should break away from the crowd. Think His thoughts. Dare to be different. Dare to think, act, and live according to His truth!