Before we render our bodies as living sacrifices to God, we have to be alive in Christ. Before we are alive in Christ Jesus, we have to understand that He died for us, all our sins, and now lives for us, lives in us.
First, we recognize that He has justified us:
"16For I am not ashamed of the gospel of Christ: for it is the power of God unto salvation to every one that believeth; to the Jew first, and also to the Greek. 17For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith." (Romans 1: 16-17)
We have to acknowledge that this righteousness cannot be earned, but is received:
"21But now the righteousness of God without the law is manifested, being witnessed by the law and the prophets; 22Even the righteousness of God which is by faith of Jesus Christ unto all and upon all them that believe: for there is no difference: 23For all have sinned, and come short of the glory of God;" (Romans 3: 21-23)
We receive this righteousness through Jesus:
"15But not as the offence, so also is the free gift. For if through the offence of one many be dead, much more the grace of God, and the gift by grace, which is by one man, Jesus Christ, hath abounded unto many. 16And not as it was by one that sinned, so is the gift: for the judgment was by one to condemnation, but the free gift is of many offences unto justification. 17For if by one man's offence death reigned by one; much more they which receive abundance of grace and of the gift of righteousness shall reign in life by one, Jesus Christ." (Romans 5: 15-17)
Notice that we "reign in life" because of the gift of righteousness. Because of that gift, we are then dead to sin:
"11Likewise reckon ye also yourselves to be dead indeed unto sin, but alive unto God through Jesus Christ our Lord.
12Let not sin therefore reign in your mortal body, that ye should obey it in the lusts thereof. 13Neither yield ye your members as instruments of unrighteousness unto sin: but yield yourselves unto God, as those that are alive from the dead, and your members as instruments of righteousness unto God. 14For sin shall not have dominion over you: for ye are not under the law, but under grace." (Romans 6: 11-14)
When we realize that we are alive because of His righteousness, then we can start being of service.
This righteousness is from Jesus:
"For he hath made him to be sin for us, who knew no sin; that we might be made the righteousness of God in him." (2 Corinthians 5: 21)
Jesus is our sacrifice, and because of Him, we can be a living sacrifice and allow Him to live in us!