Much of the conversation often focuses on Joseph Smith's supposed translation and whether or not it was miraculous. I do not discount those arguments, as they are important, but I feel that there is a much more important topic to touch upon: the spiritual testimonies that the Book of Mormon contain.
To me, who wrote and/or translated the Book of Mormon is of little immediate concern. I am more concerned to let the book speak for itself. There have been genius works written by complete nobodies, and there have been complete duds written by alleged geniuses. I care more about what the text has to say about the Divinity of Jesus Christ than where it came from. If it can support itself on that regard, then clearly it comes from God, for as the psalmist says, "I say to the Lord, ‘You are my Lord; apart from you I have no good thing.'" (Psalm 16:2, NIV).
Indeed, Professor Hugh Nibley (who is about as "apologetic" as one can get concerning the restored Gospel of Jesus Christ) states:
Indeed, the Book of Mormon is quite impossible on that ground [the thesis that Joseph Smith wrote it]. The fact that it exists proves that somebody wrote it, but not necessarily that Joseph Smith did.... He is an exceedingly unlikely candidate, but where will you find a more likely candidate? 
Similarly, Elder Jeffrey R. Holland, who members of the Church of Jesus Christ of Latter-day Saints believe to be an modern-day Apostle with the same authority as the apostles in the New Testament, makes the argument (albeit quoting his grandfather) that “No wicked man could write such a book as this; and no good man would write it, unless it were true and he were commanded of God to do so.” 
Much of his writing and speaking focuses on that idea: prove the Book of Mormon's testimony of Jesus Christ before trying to prove anything about where it came from. If the book testifies of Christ as profoundly as it does, then no evil man could have written it, and a good man would have only if divinely inspired of God.
For the apologist, this provides two main advantages: (1) showing that the book testifies of Christ is easy, and (2) it is much easier to reason about the book's origin having established that somehow it came from God.
The Book of Mormon is Another Testament of Jesus Christ
Before arguing that the Book of Mormon testifies of Jesus's divinity, one must first prove that the book talks about him at all. Luckily, this is easy. Citing an essay on the Church of Jesus Christ of Latter-day Saints's website:
The Book of Mormon is another witness of Jesus Christ and confirms the truths found in the Holy Bible. Far from undermining the Bible, the Book of Mormon supports its testimony of Jesus Christ. One passage says that the Book of Mormon “shall establish the truth” of the Bible “and shall make known to all kindreds, tongues, and people, that the Lamb of God is the Son of the Eternal Father, and the Savior of the world; and that all men must come unto him, or they cannot be saved” (1 Nephi 13:40).
In its more than 6,000 verses, the Book of Mormon refers to Jesus Christ almost 4,000 times and by 100 different names: “Jehovah,” “Immanuel,” “Holy Messiah,” “Lamb of God,” “Redeemer of Israel,” and so on. 
Doing a little bit of math shows that the Book of Mormon mentions Jesus Christ (by some title) on average every 1.7 verses. Why would a book reference Him every other verse, if not to testify of his divinity?
Simply mentioning someone that frequently, in and of itself, does not show that the book favors that person. Perhaps, those references attempt to discredit the Savior, as many critics of the Book of Mormon tend to believe. But the Book of Mormon is clear in this regard as to its purpose. Nephi, the first writer in the text, expresses this clear intent multiple times in his chapters.
26 And we talk of Christ, we rejoice in Christ, we preach of Christ, we prophesy of Christ, and we write according to our prophecies, that our children may know to what source they may look for a remission of their sins. 
4 And I know that the Lord God will consecrate my prayers for the gain of my people. And the words which I have written in weakness will be made strong unto them; for it persuadeth them to do good; it maketh known unto them of their fathers; and it speaketh of Jesus, and persuadeth them to believe in him, and to endure to the end, which is life eternal.
5 And it speaketh harshly against sin, according to the plainness of the truth; wherefore, no man will be angry at the words which I have written save he shall be of the spirit of the devil.
6 I glory in plainness; I glory in truth; I glory in my Jesus, for he hath redeemed my soul from hell. 
Thus, we clearly see that the intent of the Book of Mormon is to convince men how to love and worship Jesus Christ and seek Him for a remission of their sins. I have omitted many references to powerful, life-changing sermons and allegories that the book contains. There is no way that someone can read this entire book and honestly claim that it does not lift up their testimony of the Savior and persuade them to do good.
Does a Testimony really imply Divine Inspiration?
Many quickly counter the above by pointing out that there are plenty of men who use Jesus's name for nefarious purpose, ergo simply speaking of Christ is not sufficient evidence of divine inspiration. While true, this counterargument confuses "testifying of Christ" with "speaking of Christ". A testimony necessarily implies an exhortation to repent and follow Jesus Christ. Does following an alleged testimony's counsel lead to happiness and peace in Jesus? Or does their encouragement lead to other paths? If the former, then it is a testimony. If the latter, then one is right to doubt whether it comes of God. Jesus himself warns of this distinction and provides that test in the Sermon on the Mount (Matthew 7:16-20, KJV):
15 ¶ Beware of false prophets, which come to you in sheep’s clothing, but inwardly they are ravening wolves.
16 Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles?
17 Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.
18 A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit.
19 Every tree that bringeth not forth good fruit is hewn down, and cast into the fire.
20 Wherefore by their fruits ye shall know them.
Jesus's sets His standard clearly. When determining whether some teaching is good and godly, look to see the fruits that will happen if you live it. Will living it bring one closer to God? Or will living it take one down "the way which leadeth to destruction" (Matthew 7:14)? If it convinces one to follow Jesus, then it did not come from a corrupt tree.
With this in mind, let us see what the fruits of following the doctrines contained in the Book of Mormon yield. For brevity's sake, I include only one exhibit: an excerpt from a sermon from Jesus himself in the Book of Mormon.
19 And no unclean thing can enter into his kingdom; therefore nothing entereth into his rest save it be those who have washed their garments in my blood, because of their faith, and the repentance of all their sins, and their faithfulness unto the end.
20 Now this is the commandment: Repent, all ye ends of the earth, and come unto me and be baptized in my name, that ye may be sanctified by the reception of the Holy Ghost, that ye may stand spotless before me at the last day. 
Here, the Master explains the doctrine and the fruits--and ultimately the central message of the Book of Mormon--very plainly. Faith, repentance, and baptism will lead to sanctification and standing spotless before God. If that is not an encouragement to follow Jesus, then I do not know what is.
The doctrines cannot simultaneously convince one to follow Jesus and to follow the Adversary. But clearly, the Book of Mormon expressly encourages its readers to follow Jesus Christ. No evil man, whether for personal gain or otherwise, would write a book so focused on following Jesus. No good man would do it and claim it to be revelation unless he was inspired and commanded of God to do so.
God Has Revealed the Divinity of the Book of Mormon to Millions, and He Can Reveal It To You, Too!
An important piece of theology and a belief crucial to members of the Church of Jesus Christ of Latter-day Saints is the concept of "personal revelation". For them, God is not a silent or passive figure in their lives. When they pray, they do not only expect God to listen to and answer prayers, but they expect him to respond and converse with them.
In a demonstration of this faith, Moroni (the final writer in the Book of Mormon) tells those who read the book to pray and ask God if it is divinely inspired. He asserts that physical arguments are incapable of granting a spiritual testimony, just as Jesus taught Peter in Matthew 16-17 ("And Jesus answered and said unto him, Blessed art thou, Simon Barjona: for flesh and blood hath not revealed it unto thee, but my Father which is in heaven.", KJV). Conversion to true Christianity has to come via revelation from the Father. In this vein, here is Moroni's counsel:
3 Behold, I would exhort you that when ye shall read these things, if it be wisdom in God that ye should read them, that ye would remember how merciful the Lord hath been unto the children of men, from the creation of Adam even down until the time that ye shall receive these things, and ponder it in your hearts.
4 And when ye shall receive these things, I would exhort you that ye would ask God, the Eternal Father, in the name of Christ, if these things are not true; and if ye shall ask with a sincere heart, with real intent, having faith in Christ, he will manifest the truth of it unto you, by the power of the Holy Ghost.
5 And by the power of the Holy Ghost ye may know the truth of all things.
6 And whatsoever thing is good is just and true; wherefore, nothing that is good denieth the Christ, but acknowledgeth that he is.
7 And ye may know that he is, by the power of the Holy Ghost; wherefore I would exhort you that ye deny not the power of God; for he worketh by power, according to the faith of the children of men, the same today and tomorrow, and forever. 
Moroni promises that if you ponder the writing in the Book of Mormon, ask God with faith, and having real intent (i.e. the intent to really repent and change one's life to better follow Christ's teachings in the Bible and the Book of Mormon), then the Holy Ghost will reveal it unto you.
Millions have untaken "Moroni's challenge", so to speak. The Church of Jesus Christ of Latter-day Saints currently has some 16 million members, and although not every one will have prayed about the divinity of the Book of Mormon specifically, my estimate would be you could ask a huge portion of them (likely >50%) about their experience doing so, and they could describe it to you.
God has revealed the divinity of the Book of Mormon to millions, and can do the same for you.
A Personal Disclaimer and Testimony
In my life, I have gone from aggressive critic of the Book of Mormon, to hesitant apologetic, and eventually to ardent believer. In the above, I highlight apologetic arguments that have been particularly impactful for me. For years, I was never sold on the historical apologetic arguments in favor of the divinity of the Book of Mormon. For a long time, one of my favorite hobbies was attacking it on those very grounds. But I eventually realized that despite my arguments, the Book still existed. After some time, I finally read it. Despite my furious efforts to find contradictions, by the end of it, I could not shake the fact that it had indeed grown my faith in Jesus Christ and his role as my personal Savior just as much as the Old and New Testaments had. I had to humble myself and ask God if the book had come from him. I immediately received a powerful, strong witness that he had indeed sent it to the Earth for that very purpose. Nothing can take that experience from me. My continued study of the Book of Mormon and Bible have taken me from the hesitant apologetic to believer in Jesus Christ that I am today.
 Hugh Nibley. The Book of Mormon as a Record of Military Strategy. https://speeches.byu.edu/talks/hugh-nibley/book-mormon-record-military-strategy/
 Elder Jeffrey R. Holland. Safety for the Soul. https://abn.churchofjesuschrist.org/study/general-conference/2009/10/safety-for-the-soul?lang=eng
 Gospel Topics. The Book of Mormon. https://abn.churchofjesuschrist.org/study/manual/gospel-topics/book-of-mormon?lang=eng
 2 Nephi 25:23. The Book of Mormon. https://abn.churchofjesuschrist.org/study/scriptures/bofm/2-ne/25.23?lang=eng&clang=eng#p23
 2 Nephi 33:4-6. The Book of Mormon. https://abn.churchofjesuschrist.org/study/scriptures/bofm/2-ne/33?lang=eng
 3 Nephi 27:19-20. The Book of Mormon. https://www.churchofjesuschrist.org/study/scriptures/bofm/3-ne/27?lang=eng
 Moroni 10:3-7. The Book of Mormon. https://abn.churchofjesuschrist.org/study/scriptures/bofm/moro/10?lang=eng