We see the truth of this doctrine in the way Christians live. If they are truly spiritually alive they will look different than those who are not.
If all of that is true (and it is), then anyone reading this who gives a rip about the condition of their own soul should be asking this question: In what ways will a real Christian look different?
If I call myself a Christian and have all my confidence before God in the work and Person of Jesus Christ, in what ways should I expect my life to look different than those who have no such faith?
There are many places in the Scriptures we could go to find an answer to this question, but in this post we're going to just look a few places in St. John's First Letter (1 John). The whole letter seems to have been written to help us distinguish those who are truly believers and those who are not. In it John gives us four signs of true spiritual life:
1. Obedience to God's Commands: "And by this we know that we have come to know Him, if we keep his commandments." (1 John 2:3) And what are God's commands? Two summaries of his requirements exist for us in the Great Commandment (love God and love neighbor) and the 10 Commandments (which tell us what loving God and our neighbor looks like). A person whose faith is real will have a life that is characterized by obedience to God. This obedience, of course, will not be perfect (see 1 John 1:8-2:1), but a true Christian is one who, when he does know he is in sin, confesses, repents, believes the Gospel, and obeys. Such a person is noticeable.
2. Love for God and other people: "Do not love the world or the things in the world. If anyone loves the world, the love of the Father is not in him... Beloved, let us love one another, for love is from God, and whoever loves has been born of God and knows God." (1 John 2:15; 4:7) A person who has no inkling of a love for God, as one loves other people, does not really have spiritual life. Neither does someone who hates God's people, that is, the Church. You may want to ask yourself, as I have had to ask myself in the past: "Do I love being with God's people? Do I love to worship with other Christians?"
3. Right Doctrine: "Whoever knows God listens to us [that is the Apostle's teaching in the Scriptures]; whoever is not from God does not listen to us. By this we know the Spirit of truth and the spirit of error." (1 John 4:6) As the Creed of Athanasius states, belief in the core doctrines of Christianity is essential to salvation, and we deviate from these core doctrines to the peril of their own soul. Core Christian doctrines spring from the Bible and are recognized in the Scriptures by the community of the Church. Anyone claiming to be a Christian who states (without ignorance) things contrary to what Christians have believed always and everywhere (see the Apostles Creed and the Nicene Creed for good summations of this) is not giving themselves or others confidence of their being truly God's.
4. The Presence of the Holy Spirit: "By this we know that we abide in him and he in us, because he has given us of his Spirit..." (1 John 4:13) God's Holy Spirit lives in all true believers (Eph 1:13; Rom 8:9), and evidences of his presence are both objective (the things listed above in items 1-3) and subjective: that because of the Holy Spirit's presence, we simply know that we are God's (Rom 8:16).
So these, in a nutshell, are the ways in which a Christian should be different. Again, this is only a very compact summary, but don't let it's simplicity cause you throw it out: simple things can be true also.
A closing thought on these four signs of life from 1 John: God gave them to us to assure us that we are His (1 John 5:13). They were meant to comfort and not to concern us. So then... Do you find these four characteristics in your life? Do not despair or get depressed if you see them only in small, freckle-sized amounts, but be assured: you are seeing God's work in your life.