In the tradition in which I was raised, you would be born-again by sincerely praying the Sinner's Prayer, of which there are several versions. This is one:
Lord Jesus, I want to know You personally. Thank You for dying on the cross for my sins. I open the door of my life and receive You as my Savior and Lord. Thank You for forgiving me of my sins and giving me eternal life. Take control of the throne of my life. Make me the kind of person You want me to be.
(From Campus Crusade for Christ's website)
I do not wish to mock the Sinner's Prayer, as I think it is an elegant compilation of what the Bible says that a life with Christ looks like. However, the key word here is "compilation." The Sinner's Prayer does not appear in the Bible. It is a relatively new development, and while I think you can commit your life to Christ by praying this prayer, I don't think it's the only way.
What it comes down to is the least common denominator. If the Sinner's Prayer is how one becomes a Christian, then what happens if you get the words wrong? For that matter, there are numerous formulations of the Sinner's Prayer. Which one is right? The general belief is that the words themselves are unimportant, as long as you pray with sincerity. Even if the exact words don't matter, do you still have to hit all the correct points: Repentance of sin, submission to God, asking to be remade? And what about understanding? You need to understand what you're praying in order to be sincere about it, right? That would disqualify the large number of young children who say this prayer before they fully understand it. And there's something disconcerting about the fact that the vast majority of those who have called themselves Christians throughout history have never heard this prayer, much less said it.
What does the Bible say about what it takes to be born again? Jesus never really explained it to Nicodemus, but he was asked about how to have eternal life on numerous occasions by plenty of people. To the rich ruler, Jesus said "You know the commandments, 'Do not commit adultery, do not murder, do not steal, do not bear false witness, honor your father and mother.'" When the ruler answered that he had done all these things, Jesus contined, "One thing you still lack; sell all that you possess and distribute it to the poor, and you shall have treasure in heaven; and come, follow Me." (Luke 18:17-30, NAS) To the lawyer, he said, "What does the law say?" The lawyer responded, "To love God with all my heart, soul, mind, and might, and to love my neighbor as I love myself." Jesus explained, "Do this and you will be saved." (Luke 10:25-28, paraphrase) When the thief on the cross said, "We deserve the punishment we receive, but this man [Jesus] has done nothing. Lord, remember me when you come into your Kingdom," Jesus replied, "Today you will be with me in paradise." (Luke 23:39-43, paraphrase) At Pentecost, when the Jews asked, "What must we do?", Peter said, "Repent and be baptized, all of you, in the name of Jesus Christ for the forgiveness of your sins. And you will receive the Holy Spirit." (Acts 2:38, NAS) In one of his letters, Paul told the Romans, "If you confess with your mouth 'Jesus is Lord,' and believe in your heart that God raised him from the dead, and you will be saved."(Romans 10:9, paraphrase)
This last one is often quoted in response to the "How do I become born-again?" question, so I'll add a little context:
But what does it say? "The word is near you, in your mouth and in your heart"--that is, the word of faith which we are preaching, that if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved; for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation. For the Scripture says, "Whoever believes in him will not be disappointed." For there is no distinction between Jew and Greek; for the same Lord is Lord of all, abounding in riches for all who call on Him; for "Whoever will call on the name of the Lord will be saved."
(Romans 10:8-13, NAS)
This is part of the Roman road to salvation, a collection of verses which spell out how one becomes saved. The full collection is:
Rom 3:23 For all have sinned, and come short of the glory of God;
Rom 6:23 For the wages of sin is death; but the gift of God is eternal life through Jesus Christ our Lord.
Rom 5:88 But God commendeth his love toward us, in that, while we were yet sinners, Christ died for us.
Rom 10:9 That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved.
Rom 10:13 For whosoever shall call upon the name of the Lord shall be saved.
Rom 12:1 I beseech you therefore, brethren, by the mercies of God, that ye present your bodies a living sacrifice, holy, acceptable unto God, which is your reasonable service.
Rom 12:2 And be not conformed to this world: but be ye transformed by the renewing of your mind, that ye may prove what is that good, and acceptable, and perfect, will of God.
This is useful, and it does cover all the components in the Sinner's Prayer above. However, I'm always a bit suspicious of seemingly random collections of verses being given as a clear step-by-step process to anything. It wasn't so clear to Paul's readers, as Paul didn't put them together in a nice compact package, as has been done here.
So looking at this huge variety of answers, what do I think it takes to be saved? What the Sinner's Prayer does is compile the elements from all these answers, to give a nice, clear prayer that should cover it all. However, no one in the Bible was ever called to pray exactly these things. In fact, a straightforward reading of the scripture might lead one to believe that if you did any of the things mentioned above, you would be saved. At the least, if you were that person in that situation and you were told to do this by Jesus or one of his apostles, then that is what you would have had to do to be saved. Does that tell us what we, or for that matter, I have to do, in order to be saved?
Let's return to Paul's answer, as it was simple and the most general, addressed to a diverse audience most of whom Paul had never met. (It was written before Paul got to Rome.) "If you confess with your mouth 'Jesus is Lord,' and believe in your heart that God raised him from the dead, you will be saved." Saying the Sinner's Prayer covers that right? In fact, pretty much anybody who's gone to church has at some point said, "Jesus is Lord," (it's in creeds, songs, prayers--you name it). Granted, not everyone who goes to church believes that Jesus rose from the dead, but I'd say that even in these post-modern times, most who regularly attend church do. Ah, but do they mean the "Jesus is Lord" part? The word after all is confess, which is a pretty accurate translation of the Greek word (homologeseis -- to agree with (I apologize in advance for the poor transliteration)). It doesn't count unless you mean "Jesus is Lord" when you say it. But what should you mean by that? In the general sense, that he really is the Son of God and has all the rights and priveleges thereof? Or in the personal sense, that he's the Lord of your life--the whole submission part of the Sinner's Prayer? But how much do we really submit, even when we mean it? It's easier said than done, which may be the reason that Paul calls on us to confess, or even admit, that "Jesus is Lord." It is not so we can mouth the words without meaning them, but by saying the words, and meaning them to the full extent that we are able, they slowly become more true in our lives.
In this sense, maybe Romans 10:9 is not so much about the sinner who, in one moment of belief and repentance, finally comes to Christ, but the imperfect Christian, who despite doubt and reluctance, day after day says "Jesus is Lord," praying that it might be truer and truer in his life. And this is where I think evangelicalism departs from fundamentalism. Not every evangelical will agree with this assessment, but many will. While there is no denying the dramatic, instantaneous salvation experience, which is attested to in both the Bible and in experience, many Christians--arguably including the Apostles themselves and definitely including all who have grown up in the Church--have experienced a growing faith and commitment where it is hard to pin down a starting point and a completion point. Most evangelicals accept the legitimacy of this salvation experience, while fundamentalists will insist on pointing to a particular moment where the Christian was born again, saying the Sinner's Prayer and having a conversion experience, in order to accept him as a true Christian.
In my own life, where I was raised in the tradition of instantaneous salvation, I would be hard pressed to point to one place where I became a Christian. Or rather, I could point to a half-dozen times while growing up where I prayed a form of the Sinner's Prayer with various degrees of understanding and sincerity. While I'd have a hard time pointing to the one and only place where I said it and meant it, I do know the point where I had fully come to mean it. If you'd like to read about it, it's in my autobiographical webpage here.