Alma gives us more information about Melchizedek than is contained in Genesis. We learn in Hebrews that Melchizedek, as the great high priest, became a type for the Savior, even Jesus, made an high priest for ever after the order of Melchisedec…who needeth not daily, as those high priests, to offer up sacrifice, first for his own sins, and then for the people’s: for this he did once, when he offered up himself (Heb 6:20; 7:27).
The rest of what we know about Melchizedek comes from Genesis, Hebrews and Joseph Smith, mostly through his translation of Genesis. Melchizedek was remarkable from his youth, when a child he feared God, and stopped the mouths of lions, and quenched the violence of fire (JST Gen 14:26). He was approved of the Lord and was ordained to the priesthood through the lineage of his fathers (DC 84:14). His city, Salem (later known as Jerusalem) became so righteous under his leadership that it approximated the righteousness of the city of Enoch, his people wrought righteousness, and obtained heaven, and sought for the city of Enoch which God had before taken (JST Gen 14:34). He became the keeper of the storehouse of God (JST Gen 14:37), and it was in this capacity that Abraham saw fit to pay him tithes.
The encounter between Melchizedek and Abraham is interesting. Abraham was returning from one of his very few military excursions when he met Melchizedek (Gen 14:14-17). Abraham recognized Melchizedek’s authority and sought for the same appointment. Melchizedek had brought him wine and bread (possibly symbolizing the sacrament, see Gen 14:18). Melchizedek became the mentor for the younger Abraham. Joseph Smith described part of their interaction, “Abraham says to Melchizedek, I believe all that thou hast taught me concerning the priesthood and the coming of the Son of Man; so Melchizedek ordained Abraham and sent him away. Abraham rejoiced, saying, Now I have the priesthood” (Teachings, p. 322-3). Paul may have been referring to his ordination when he explains that Abraham was blessed of Melchizedek (Heb 7:6). Alma explains that among high priests, there were none greater (v. 19) and this is the reason why the higher priesthood was named after him (DC 107:2).
Robert Millet and Joseph Fielding McConkie elaborate on how Melchizedek is a type for Christ:
"In these verses (v. 17-19) Alma establishes Melchizedek as a type for Christ, noting the following parallels: First, like Christ, he was a king. The very name of this great high priest - Melchizedek, ‘king of righteousness’, perhaps more correctly, ‘my king is righteousness’-affirms and testifies of the goodness and power of the coming Messiah. Righteousness is also a name-title of Christ (see Moses 7:45). As Melchizedek ruled his kingdom in righteousness, so Christ will eventually rule and reign upon this earth, doing so with the unchanging scepter of righteousness and truth, possessing an everlasting dominion without compulsory means (see D&C 121:46).
"Second Melchizedek ruled over the city of Salem (a name which means ‘peace’). In like manner, Christ will reinstitute the glory of David‘s day when nought is known but peace among the Lord’s people. Third, both Melchizedek and Christ were known as the ’great high priest.’ In Old Testament times the primary duty of the priest was to offer sacrifice at the altar and to act as mediator between God and men. It was by virtue of the priestly functions that the nations of Israel were reconciled to their God. ’Through the ministrations of the priesthood the people of Israel were instructed in the doctrine of sin and its expiation, in forgiveness and worship. In short, the priest was the indispensable source of religious knowledge for the people, and the channel through which spiritual life was communicated.’ (International Standard Bible Encyclopedia 4: 2439.)
“Fourth, both were men of ‘mighty faith’ who taught ‘repentance’ to their people. Of Melchizedek we read, ’his people wrought righteousness, and obtained heaven’ (JST, Genesis 14:34). And of course the same will be true of all who sustain Christ and his teachings in righteousness. Fifth, both bore the title Prince of Peace, being teachers of that gospel by which peace and joy come. Sixth, of Melchizedek we read, ’and he did reign under his father,’ as does Christ, who professes no authority save that of his Father (see John 5:30). Seventh, though there were many prophets before Melchizedek and many after him, Alma described the king of Salem by saying ’none were greater.’ Thus this great prophet, priest, and king stood as a classic type of the Promised Messiah, of whom it is true not only that none were greater, but also that none have been as great.” (McConkie and Millet, Doctrinal Commentary on the Book of Mormon, vol. 3, pp. 102-3)