When God changed us at salvation, we were changed from sinners to children of God. He changed not just what we do, he changed who we are. A truly converted Christian will have fundamentally different behavior than an unconverted sinner. From the book of I John, there are four different proofs of a Christian's salvation.
A true Christian will have the Holy Spirit. At salvation, the Christian becomes indwelled by the Holy Spirit. The Holy Spirit will bring the fruit found in Galatians 5:22-23. Love, joy, peace, patience, kindness, goodness, and faith will all be the fruit that a Spirit filled Christian has in his life.
A true Christian will not follow after false doctrine. Most Christians do not struggle with right doctrine. Some, however, will get caught up in books like The Shack and Velvet Elvis: books that look good, and sound good but are filled with things that aren't true. Beware of anyone who doesn't believe that Christ was God or that Mary was a virgin when she was pregnant with Christ.
A true Christian will love other Christians. He will enjoy having fellowship with other people who believe the same thing as he does. Someone who is converted will go to church when he can. Someone who avoids church should check out his salvation. Someone who is converted will not hate a brother in Christ.
A true Christian will not love the sin that is in the world and make a practice of sinning. Preachers often use I John 2:15-17 about how Christians should not love the world. John is saying that Christians should not love sin, not necessarily things that aren't sinful but are part of the world.
When we are converted, we will will not continue to sin without conviction. Lot lived for years in one of the most wicked cities in the world, and II Peter 2:7 says Lot was greatly distressed with the sin around him. If you sin consistently, without conviction or regret, you according to the Bible, are probably not saved.