If a person has true faith, but has not been baptized.
Are they born again?
If your answer is yes, then explain where the "born of water" part fits into the persons faith.
Well, after we are saved by God's grace (Jesus Christ) by faith, I believe works of faith are necessary to show a person's faith is genuine and that the Lord lives within a person. For it is the Lord who works within us. No Jesus living in us and no salvation (1 John 5:12). Most teach a form of greasy grace these days. They think you can commit grievous sin and still be saved. Some will even say holiness is necessary but yet they believe one unconfessed grievous sin cannot separate a person from God. This is wrong. Then again, they are not fooling anyone. It's pretty easy to figure out that we have to be good as a part of being in God's Kingdom. But most do not want to be good.
Then there are those who think we have to obey the Old Law to be saved like the Saturday Sabbath, etc. This is also a major problem, as well; And it is seeking to make laws as a requirement that are no longer binding anymore. This is bondage.
As for water baptism:
Well, I have been baptized and I do believe it is very important for every believer to do this because I feel it helps their spiritual walk with God. But is baptism for salvation? Peter says in 1 Peter 3:21 that baptism does not save in regards to the putting away of the filth of the flesh. The words "filth of the flesh" is in reference to "sin." For similar words "filthiness of the flesh" is clearly used in reference to sin in 2 Corinthians 7:1. So Peter is saying that baptism does not save us in putting away sin. So what about all the baptism and you are saved verses? Those verses are talking about being baptized by the Spirit (Which is a part of being born again and having a new heart).
So what does being born of water mean?
Ephesians 5:25-26 says,
"...even as Christ also loved the church, and gave himself for it;
That he might sanctify and cleanse it with the washing of water by the word,..."
Jesus said,
"Now
ye are clean through the word which I have spoken unto you."
(John 15:3).
"Wherewithal shall a young man
cleanse his way? by taking heed thereto according to thy word." (Psalms 119:9).
"Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever." (1 Peter 1:23).
"So then faith
cometh by hearing, and hearing by the word of God." (Romans 10:17).
In the Parable of the Sower, we learn that the seed is the Word of God (Luke 8:11) and the Sower is the Son of Man (Matthew 13:37). The seed is sown in our heart. This is the good news from the Holy Scriptures (or our receiving of the gospel and Christ).
So in conclusion:
Being born again by the Spirit is being regenerated by the Holy Spirit and being born again by the water is being born again by hearing the Holy Scriptures (that made you repent of your sins to the Lord Jesus Christ in the first place). A person needs to hear or read Scripture in some way in order to repent and accept Jesus. They cannot accept some other holy word or book. They are born again by God's Word. They had a spiritual experience when reading or listening to God's Word.