I learned about it following Mitt Romney last election. The biggest thing I learned is that it's completely, transparently false.
There is no reason to believe that Joseph Smith was anything like a prophet. There is plenty of reason to believe he was a fraud. As a youth, he was locally known for his tall tales and con jobs. As a young man, he was well versed in the occult practices common in the region and was acquainted with Swedenborg's New Church ideas, such as multiple levels of Heaven and marriage in the afterlife. As an adult, he suddenly appeared with this alleged record of prehistoric upstate New York written in Hebrew using the Egyptian alphabet that he refused to let more than a few people see. He translated it with his "peep stones" by putting them in a hat, putting his face in the hat, and yelling words to his friend and "scribe" behind a curtain. The resulting book bore suspicious similarity to his favorite historical fiction.
There is no physical or cultural evidence that the civilizations in the Book of Mormon ever existed outside its pages. There are no records of them among any indigenous people. There are no artifacts or ruins where the cities supposedly were. There are no bodies or weapons where the battles were supposedly fought. This isn't for lack of trying to find them. Plenty of people have. All LDS-themed archaeology has ever turned up have been new hypotheses to explain away the stark lack of evidence about what should be the most concrete, irrefutable proof for their religion.
The other records, like the Book of Abraham, are known frauds. It's now proven that Joe Smith didn't know a word of Egyptian, or even its writing system. Several of his screw ups prove this. One is his lesser known works, Egyptian Alphabet & Grammar, has been thoroughly wrecked by actual Egyptologists. Another, and probably the most damning, is his mistake regarding the Kinderhook plates. Those are a set of six plates brass plates some farmers forged to trick him into trying to translate them. He took the bait.
There are other problems with his credibility as well, like his multiple versions of his "first vision" story and his criminal record. I just don't understand it. How can anyone look at this religion and see anything but a couple centuries old fraud ultimately made up by a shameless huckster looking to build a cult of personality around himself and score himself some married 14 year old poon?