Alvin was born 11 February 1798 in Tunbridge, Orange County, Vermont to Joseph Smith (1771-1840) and Lucy Mack (1775-1856) and died 19 November 1823 Bilious colic illness of mercury poisoning from calomel.
Eldest brother of Joseph Smith, Jr., the founder of the Latter Day Saint movement. Alvin took a leading role in helping the Smith family work toward paying their debts and building their home. His death in 1823 at age 25 resulted in his younger brother Joseph taking more of a leading role in family affairs. A vision claimed by Joseph Smith Jr. is said to have included Alvin and played a significant role in the establishment of the Mormon doctrines of redemption of those who die without a knowledge of the gospel and baptism of the dead.
Smith was born in 1798, the first surviving child of Joseph Smith, Sr. and Lucy Mack Smith. During his youth, Alvin worked as a carpenter’s helper to assist the Smith family in saving up sufficient funds to make a down payment on a farm in Manchester Township, south of Palmyra, New York. Alvin also assisted his father in clearing timber, planting wheat and tapping maple trees for the purpose of making maple sugar. A neighbor, Orlando Saunders, stated that the members of the Smith family “have all worked for me many a day; they were very good people. Young Joe (as we called him then) has worked for me, and he was a good worker; they all were.” In 1823, Alvin took the lead in building the Smith’s new home and worked to get the family out of debt.
On 19 November 1823, at age 25, Alvin died of mercury poisoning from calomel, which was administered to cure a case of “bilious colic.” Alvin believed his brother Joseph's claim that he was to recover an ancient record from a nearby hill. His death occurred two months after Joseph’s first visit to the hill from which he was eventually said to have recovered the golden plates that would later be claimed to be the source for the Book of Mormon. According to a history written by his mother, Lucy Mack Smith, as Alvin lay dying he called each member of his family to his bedside to give them counsel. To his brother Hyrum, Alvin said, "I have done all I could to make our dear parents comfortable. I want you to go on and finish the house." He urged his younger brother Joseph to fulfill all of the requirements to obtain the record.
Then one autumn morning, less than two months after Moroni’s visit, Alvin came home with an intense pain in his stomach. Bent over in agony, he begged his father to call for help. When a doctor finally arrived, he gave Alvin a large dose of a chalky medicine, but it only made things worse.
Alvin lay in bed for days, writhing in pain. Knowing he would probably die, he called for Joseph. “Do everything that lies in your power to obtain the records,” Alvin said. “Be faithful in receiving instruction and keeping every commandment that is given you.”27
He died a short time later, and sorrow settled over the house. At the funeral, a preacher all but said Alvin had gone to hell, using his death to warn others of what would happen unless God intervened to save them. Joseph Sr. was furious. His son had been a good young man, and he could not believe that God would damn him.28
With Alvin gone, talk of the plates ended. He had been such a staunch supporter of Joseph’s divine call that any mention of them brought his death to mind. The family could not bear it.
Joseph missed Alvin terribly and took his death especially hard. He had hoped to rely on his oldest brother to help him get the record. Now he felt forsaken. 
Smith figured prominently in the establishment of the Mormon doctrine of the redemption of the dead and later establishment of the practice of baptism for the dead. On January 21, 1836, after the completion of the Kirtland Temple, Joseph Smith claimed to have had a vision of the celestial kingdom. Smith stated that he saw his brother Alvin in the vision, and was surprised at his presence there since he died before the establishment of the church and its associated doctrines.
D&C 137:1-9 - The heavens were opened upon us, and I beheld the celestial kingdom of God, and the glory thereof, whether in the body or out I cannot tell. I saw the transcendent beauty of the gate through which the heirs of that kingdom will enter, which was like unto circling flames of fire; Also the blazing throne of God, whereon was seated the Father and the Son. I saw the beautiful streets of that kingdom, which had the appearance of being paved with gold. I saw Father Adam and Abraham; and my father and my mother; my brother Alvin, that has long since slept; And marveled how it was that he had obtained an inheritance in that kingdom, seeing that he had departed this life before the Lord had set his hand to gather Israel the second time, and had not been baptized for the remission of sins. Thus came the voice of the Lord unto me, saying: All who have died without a knowledge of this gospel, who would have received it if they had been permitted to tarry, shall be heirs of the celestial kingdom of God; Also all that shall die henceforth without a knowledge of it, who would have received it with all their hearts, shall be heirs of that kingdom; For I, the Lord, will judge all men according to their works, according to the desire of their hearts.
A few months after Alvin's death, rumors circulated that his grave had been desecrated (due to a lot of persecution directed against the Smith family relative to the stories about the Golden Plates shown to his brother Joseph). His father went out to inspect the grave and published an official notice in the local paper, Wayne Sentinel in Palmyra, Wayne County, New York:
Wayne Sentinel - September 29, 1824: TO THE PUBLIC: Whereas reports have been industriously put in circulation that my son Alvin had been removed from the place of his interment and dissected; which reports ... are peculiarly calculated to harrow up the mind of a parent and deeply wound the feelings of relations ... therefore, for the purpose of ascertaining the truth of such reports, I, with some of my neighbors this morning, repaired to the grave, and removing the earth, found the body, which had not been disturbed. This method is taken for the purpose of satisfying the minds of those who may have heard the report, and of informing those who have put it in circulation, that it is earnestly requested they would desist therefrom.
- Source Document - SidneyRigdon.com
The Salamander Letter was a fake document created by Mark Hoffman in the 1980s that circulated some false rumors regarding the desecration of Alvin's grave and Joseph's participation in necromancy to obtain the Gold Plates used for the translation of the Book of Mormon.
- 1798-Feb-11 : Vermont Vital Records - Birth of Alvin Smith at Tunbridge VT.
- [www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=6333883 Gravesite of Alvin Smith] - FindAGrave Memorial #6333883
- Biography of Alvin Smith - Wikipedia Article
- History of Alvin Smith - The most detailed historical sketch of Alvin can be found here at the Joseph Smith Sr Historical Family Archives.
- Allen & Leonard - The Story of the Latter-day Saints
- Lucy Mack Smith - The History of Joseph Smith