From where did the Book of Abraham come and how did it become part of LDS Scripture?

Sigh... the reference manuals and official sources say it so much better than do I... So here's some quotes and links.

From the Introductory Note of the Pearl of Great Price:

The Book of Abraham. A translation from some Egyptian papyri that came into the hands of Joseph Smith in 1835, containing writings of the patriarch Abraham. The translation was published serially in the Times and Seasons beginning 1 March 1842, at Nauvoo, Illinois. (See History of the Church, 4:519–34.)

An institute student manual has more to say on the subject:

How Did the Church Obtain the Book of Abraham?

On 3 July 1835 a man named Michael Chandler brought four Egyptian mummies and several papyrus scrolls of ancient Egyptian writings to Kirtland, Ohio. The mummies and papyri had been discovered in Egypt several years earlier by Antonio Lebolo. Kirtland was one of many stops in the eastern United States for Chandler’s mummy exhibition. Chandler was offering the mummies and rolls of papyrus for sale and, at the urging of the Prophet Joseph Smith, several members of the Church donated money to purchase them. In a statement dated 5 July 1835, Joseph Smith, declaring the importance of these ancient Egyptian writings, recorded: “I commenced the translation of some of the characters or hieroglyphics, and much to our joy found that one of the rolls contained the writings of Abraham. . . . Truly we can say, the Lord is beginning to reveal the abundance of peace and truth” ( History of the Church, 2:236).

This article by Dr. Andrew Skinner of Brigham Young University goes into more detail (formatting lost in the copy operation):

In the year 1799, an intensified interest in ancient Egypt was kindled in the Western world when the Rosetta Stone was discovered near Alexandria, Egypt. Made of black basalt, the stone was found by an officer of Napoleon’s engineering corps. It bore inscriptions in three ancient languages—Egyptian hieroglyphics, demotic (a simplified script that succeeded hieroglyphics), and Greek. Among the European linguists who began to work on deciphering these inscriptions was the young French scholar Jean Francois Champollion. Hieroglyphics, the written language of ancient Egypt, had been a riddle to scholars for many centuries. Working from clues found in the last inscription on the Rosetta Stone, written in Greek, Champollion was finally able to decipher the other two inscriptions. In 1822 he published the results of his work and the science of Egyptology was born, allowing scholars to begin to read the most ancient texts of Egypt. 3

These developments involving the Rosetta Stone and Champollion contributed to the coming forth of the book of Abraham in a significant way. As one writer put it, during the early 19th century “worldwide interest in Egyptian antiquities fanned itself to a searing blaze. Egypt was soon overrun with scientific expeditions, adventurers, soldiers of fortune, and robbers of catacombs and ancient burial sites.” 4 Into this atmosphere entered Antonio Lebolo, an Italian excavator of Egyptian antiquities.

According to Oliver Cowdery’s account written in 1835, Lebolo and his work crew had discovered several mummies in one of the catacombs near the place where once stood the renowned Egyptian city of Thebes. 5 After Lebolo’s death, these mummies and two papyrus rolls and some papyrus fragments that had been placed in some of the sarcophagi eventually found their way to New York City and then into the hands of Michael Chandler. 6 He was told that no one could translate the papyri’s inscriptions. He learned, however, that a man named Joseph Smith Jr. claimed some kind of special power that allowed him to decipher ancient writings. The Prophet’s name continued to come up, mostly in derision, at the various places where Chandler stopped to display his traveling mummy show. 7 In 1835 Chandler finally made contact with the Prophet Joseph Smith in Kirtland, Ohio. An entry in the Prophet’s history dated 3 July 1835 reads:

“On the 3rd of July, Michael H. Chandler came to Kirtland to exhibit some Egyptian mummies. There were four human figures, together with some two or more rolls of papyrus covered with hieroglyphic figures and devices. As Mr. Chandler had been told I could translate them, he brought me some of the characters, and I gave him the interpretation.” 8

The Prophet Joseph Smith was then inspired to raise money to purchase Chandler’s mummies and the accompanying papyri even though he did not know exactly what the writings would disclose. Kirtland Saints contributed the funds for the purchase. The price was $2,400—not an inconsequential sum considering that the temple was under construction, but the faith of members who knew the Prophet and his works led them to help. 9

After the purchase, the Prophet Joseph began to translate some of the papyri with the assistance of scribes W. W. Phelps and Oliver Cowdery. (Warren Parish was later called and employed as scribe.) This is what the Prophet recorded in his personal history: “With W. W. Phelps and Oliver Cowdery as scribes, I commenced the translation of some of the characters or hieroglyphics, and much to our joy found that one of the rolls contained the writings of Abraham, another the writings of Joseph of Egypt, etc.,—a more full account of which will appear in its place, as I proceed to examine or unfold them. Truly we can say, the Lord is beginning to reveal the abundance of peace and truth.” 10

There is no doubt that the Prophet Joseph Smith regarded the manner in which these writings came to him as the result of divine intercession. The testimony of W. W. Phelps is no less certain: “God has so ordered it that these mummies and writings have been brought in the Church.” 11 This happened only after the Lord had prepared his Church and the world to receive the book of Abraham. The rekindled spirit of excitement about ancient Egyptian writings in the 19th century, owing to the discovery of the Rosetta Stone and Champollion’s work, was one step in that preparation. Speaking of the way the Lord has guided discoveries and achievements of the human family to further his purposes, President Joseph Fielding Smith said:

“There has never been a step taken from that day [ancient times] to this, in discovery or invention, where the Spirit of the Lord … was not the prevailing force, resting upon the individual, which caused him to make the discovery or the invention. … Nor did the Lord always use those who have faith, nor does he always do so today. He uses such minds as are pliable and can be turned in certain directions to accomplish his work, whether they believe in him or not. …

“Now, do you think that these discoveries and inventions … have come just because these men have been sitting down and concentrating their minds upon these matters and have discovered them though their thought or accidentally? Not in the least, but the Spirit of the Lord, the Light of Christ, has been back of it. … We are ready for these discoveries, these inventions, and they all have a bearing upon the restoration of the gospel and preparation for the time which is yet future, but which is shortly to come, when Christ shall reign on the earth, and for a thousand years peace shall be established.” 12

Hence, this remarkable book of Abraham was brought forth in a remarkable way to help prepare us for the Second Coming of the Savior.

I recommend following the cited cross-references (History of the Church, and other linked documents and articles) because the information in them is fascinating history and they go into much more detail.