Genesis 14

Briefly in the Old Testament, we hear about Melchizedek where -

"...Melchizedek king of Salem brought forth bread and wine: and he was the priest of the most high God.
19 And he blessed him, and said, Blessed be Abram of the most high God, possessor of heaven and earth:
20 And blessed be the most high God, which hath delivered thine enemies into thy hand. And he gave him tithes of all."  (Old Testament | Genesis 14:18 - 20)

There is very little more mentioned in the Bible except where David (Psalms) and Paul (Hebrews) spoke concerning an order after Melchizedek.

It is in the Joseph Smith Translation (JST) of the Bible in and in modern revelation that we learn a great deal more concerning this great man.  First, it is helpful to understand that -

“Melchi” means “king,” and “zedek” means “righteousness.”  (Ridges, David J. (2008-05-21). The Old Testament Made Easier - Part 1)

Thus, referring to Melchizedek, we know he was called such because he was a king of righteousness.  We learn in the JST that (I have intentionally included bracketed comments by David J Ridges) -

"And Melchizedek, king of Salem, brought forth bread and wine; and he break bread and blest it; and he blest the wine, he being the priest of the most high God,
18 And he gave  to Abram, and he blessed him, and said, Blessed Abram, thou art a man of the most high God, possessor of heaven and of earth;
19 And blessed is the name of the most high God, which hath delivered thine enemies into thine hand.
20 And Abram gave him tithes of all he had taken [all he had added to his wealth, as a result of winning the battle and rescuing lot].
21 And the king of Sodom said to Abram, Give me the persons, and take the goods to thyself.
22 And Abram said to the king of Sodom, I have lifted up my hand unto the Lord, the most high God, the possessor of heaven and earth.
23 And have sworn [covenanted] that I will not take of thee from a thread even to a shoe-latchet, and that I will not take anything that is thine, (lest thou shouldest say, I have made Abram rich;)
24 Save only that which the young men have eaten, and the portion of the men which went with me, Aner, Eschol, and Mamre; let them take their portion.
25 And Melchizedek lifted up his voice and blessed Abram.
26 Now Melchizedek was a man of faith, who wrought righteousness [who did works of righteousness]; and when a child he feared God, and stopped the mouths of lions, and quenched the violence of fire.
27 And thus, having been approved of God, he was ordained an high priest after the order of the covenant which God made with Enoch,
28 It being after the order of the son of God [it is the same priesthood that Jesus Christ holds]; which order [priesthood] came, not by man [not man-made], nor the will of man; neither by father nor mother; neither by beginning of days nor end of years [the priesthood is an eternal power]; but of God;
29 And it was delivered unto men by the calling of his [Christ’s] own voice [men do not take it upon themselves, rather, must be properly called and ordained], according to his own will, unto as many as believed on his name [in other words, the high priesthood is part of the full gospel of Jesus Christ].
30 For God having sworn unto [covenanted with] Enoch and unto his seed [posterity] with an oath by himself [as is the case with the “Oath and Covenant of the Priesthood, “detailed in D& C 84: 33– 41]; that every one being ordained after this order [the Melchizedek Priesthood] and calling should have power, by faith, to break mountains, to divide the seas, to dry up waters, to turn them out of their course;
31 To put at defiance the armies of nations, to divide the earth, to break every band, to stand in the presence of God; to do all things according to his will, according to his command, subdue principalities and powers; and this by the will of the Son of God which was from before the foundation of the world [who became the Redeemer in the premortal realm].
32 And men [such as Enoch] having this faith, coming up unto this order of God [having attained the office of high priest in the Melchizedek Priesthood], were translated and taken up into heaven.
33 And now, Melchizedek was a priest of this order [a high priest]; therefore he obtained peace in Salem, and was called the Prince of peace.
34 And his people wrought righteousness [became righteous, as shown by their good works], and obtained heaven, and sought for the city of Enoch which God had before taken, separating it from the earth [taking it up to heaven], having reserved it unto the latter days, or the end of the world [the time of the Second Coming, when it will return to earth to join Zion, the New Jerusalem— see Moses 7: 62– 63];
35 And hath said, and sworn with an oath [covenanted and promised], that the heavens and the earth should come together [perhaps a reference to the fact that the Church in heaven will join the Church on earth at the time of the Second Coming and Millennium— see D& C 65: 6]; and the sons of God should be tried so as by fire.
36 And this Melchizedek, having thus established righteousness, was called the king of heaven by his people, or, in other words, the King of peace [he was a “type” of Christ].
37 And he lifted up his voice, and he blessed Abram, being the high priest, and the keeper of the storehouse of God;
38 Him whom God had appointed to receive tithes for the poor.
39 Wherefore [this is why], Abram paid unto him tithes of all that he had, of all the riches which he possessed, which God had given him more than that which he had need.
40 And it came to pass, that God blessed Abram, and gave unto him riches, and honor, and lands for an everlasting possession [the earth will become the celestial kingdom for the worthy Saints who have lived on it (see D& C 130: 9– 11); thus, Abraham and those who enter faithfully into the Abrahamic covenant will literally have it for “an everlasting possession”]; according to the covenant which he had made [the Abrahamic covenant], and according to the blessing wherewith Melchizedek had blessed him. (JST Genesis 14:17 - 40)

There is much said in these verses.  One being that in verses 30 and 31 the power of the high priesthood is described, but I note the condition "...to do all things according to his will, according to his command, subdue principalities and powers; and this by the will of the Son of God..." because it is His order. 

Some believe that the named "righteous king" (Melchizedek) was truly Shem, son of Noah.  This seems to make sense to me because of Abraham's allegiance to this king.  I even note that in modern day we learn that -

"Abraham received the priesthood from Melchizedek, who received it through the lineage of his fathers, even till Noah;"  (Doctrine and Covenants | Section 84:14)

We here little after these verses in Genesis about Melchizedek.  In verse 34, we possibly learn why in that Melchizedek and the kingdom of Salem may have joined the City of Enoch or Zion.