The late Gordon B. Hinkley, president of LDS, speaking in an interview with PBS stated concerning Joseph Smith's alleged vision of God and Christ:

"We declare without equivocation that God the father and his son, the Lord Jesus Christ, appeared in person to the boy, Joseph Smith. Our whole strength rests on the validity of that vision." 3

:"...it's either true or false. If it's false, we're engaged in a great fraud. If it's true, it's the most important thing in the world. Now, that's the whole picture. It is either right or wrong, true or false, fraudulent or true. And that's exactly where we stand, with a conviction in our hearts that it is true: that Joseph went into the [Sacred] Grove; that he saw the Father and the Son; that he talked with them; that Moroni came; that the Book of Mormon was translated from the plates; that the priesthood was restored by those who held it anciently. That's our claim. That's where we stand, and that's where we fall, if we fall. But we don't. We just stand secure in that faith. 4

In 1823, at the age of 17, he received three visitations from Moroni (some texts say Nephi) at the time of the Autumn Equinox. The angel revealed to Joseph the location of golden tablets on which was written the history of two early American tribes. He went to the site and found: A breastplate, such as might have been worn by an ancient Israelite.
Golden plates upon which ancient American authors Ether, Mormon, Lehi and Nephi had recorded additions to Biblical history
The Urim and Thummim. These were two "stones in silver bows" which appear in Numbers 27:21 and 1 Samuel 28:6 of the Hebrew Scriptures. They were apparently devices (perhaps in the form of flat stones) that the high priest consulted to determine the will of God. They might have worked something like a pair of dice. Smith claimed that through the stones "and by the gift and power of God" he was able to translate the unknown script on the golden plates into English
Brass plates upon which another author, Laban, had quoted from Hebrew Scriptures and recorded genealogies.

However, he was not permitted to remove the plates at that time. He was instructed to return to the spot at each Autumn Equinox. Four years later, in 1827, he was finally allowed to take possession of the material.

Translation of the golden plates:

br>A friend of Smith, Martin Harris, attempted to authenticate the tablets by taking copies of some of the inscriptions to Professor Charles Anton and is said to have received verbal confirmation that the tablets were written in "reformed Egyptian" hieroglyphics. No such language exists.

Prof. Anton later denied making this statement, and wrote that the symbols that he saw were a combination of Greek, Hebrew, inverted or sideways Roman letters, and elements from a Mexican calendar.

Joseph Smith positioned himself behind a curtain and used the special stones to translate the inscriptions on the golden plates. Emma Smith, Martin Harris and Oliver Cowdery served at various times as a scribe. A 116 page Book of Lehi was translated over a two month interval.

Unfortunately, Martin Harris showed the only copies to his wife who promptly "lost" them. Lucy Harris was a skeptic, and there is speculation that she believed the book to be a fraud. By forcing Smith to retranslate the book, she hoped to demonstrate discrepancies between the two versions, thus proving that the book was a hoax. Smith stated that God was so angry at this loss that he temporarily took away the special stones. Smith later translated the plates of Nephi which described the same events as the Book of Lehi.

Mormons believe that John the Baptist later appeared to Smith and Cowdery, investing them in the Aaronic Priesthood showing them how to baptize each other by total immersion in water.

Later, the Apostles Peter, James and John invested Smith and Cowdery in the Melchizedec priesthood and commissioned them as the first two elders of the new church.

This seems here to be a merging of the Old and New Testament theology.  The priesthood of Aaron, established by God after he gives the instructions to Moses concerning the tabernacle was the Aaronic priesthood.  It ceased on the day of Jesus' crucifixion when the curtain to the inner chamber in the temple was ripped asunder, giving man direct access to God and making each believer a priest.

As for the Melchizedician priesthood, only one person is ever mentioned in the Bible as being of that priesthood and that was Jesus.  There is a reference in Genesis that a priest named Melchizedek came out to greet Abraham when he camps outside the village that later became Jeruselum.  He and Abraham break bread and share wine on the very hill where Jesus later is crucified.  Most scholars believe this actually was Christ and that it foreshadows his death and the Lord's supper.