How Did the Book of Jasher Know?
The Book of Jasher includes details about antediluvian patriarchs which are confirmed by modern revelation. The question arises of how the author of Jasher could have known specific facts from before the Great Flood, such as Cainan becoming very wise when he was forty years old. These correlations attest that it was composed from exceedingly ancient reliable sources.
The Book of Jasher has been popular among members of the L.D.S. Church as a supplement to their study of the Old Testament ever since its publication was announced in the Times and Seasons in June, 1840. Because the Church is now commencing study of the Old Testament again this month, it seems appropriate to reconsider just how authentic that book really is.
The book is a history of the world from the creation until the period of the Judges in Israel. It contains much more information than is found in Genesis for that same period, which makes very interesting reading and clears up many confusing issues in the Bible. It is written mostly as a secular history, but it does contain many references to what God was doing. It is similar to the Books of Joshua through Chronicles in the Bible which describe many historical events such as battles and wars, but which also point out the hand of God in the affairs of men.
Perhaps the closest approach to an official acknowledgment of the Book of Jasher among the latter-day saints was when the Prophet Joseph Smith quoted from it as a source which had “not been disproved as a bad author.” The saints became more enamored with the book than did the rest of the Judeo-Christian world, and certain members of the Church secured the copyright and republished the work in 1887 in Salt Lake City. Various photocopy reprints of that edition are still available, and the book is also accessible in its entirety on the internet.
The L.D.S. Church has never taken an official stand on the authenticity of the Book of Jasher, but when apostles make lists of “lost books” from the Bible, Jasher is generally included. One article in the “I Have a Question” column of The Ensign responded to the question of its authenticity. After reviewing the standard scholarly analysis of how the book appears to have been composed of old Jewish legends, the article concluded with the wise injunction to treat it according to the Lord’s advice on how to study the Aprocrypha:
Verily, thus saith the Lord unto you concerning the Apocrypha — There are many things contained therein that are true, and it is mostly translated correctly; There are many things contained therein that are not true, which are interpolations by the hands of men. Verily, I say unto you, that it is not needful that the Apocrypha should be translated. Therefore, whoso readeth it, let him understand, for the Spirit manifesteth truth; And whoso is enlightened by the Spirit shall obtain benefit And whoso receiveth not by the Spirit, cannot be benefitted. Therefore it is not needful that it should be translated. Amen. 
Anyone who has read the Book of Jasher will agree that it certainly contains much truth (many stories from the Bible), and it certainly appears to contain some later interpolations of men, so reading by the Spirit seems like an excellent way to discern which is which.
Speaking of the Apocrypha, have you read it? Do you even have a copy of it? Just what is the Aprocrypha anyway? It is important to distinguish between “apocryphal” books in general and “the Aprocrypha” with a capital “A.” An aprocryphal book can refer to almost any allegedly sacred writing not included in sacred canon and of doubtful authorship or authenticity. The Aprocrypha, on the other hand, refers to a specific collection of books which was included in the translation of the Hebrew Old Testament into Greek in the third century BC (the Septuagint), but which was later rejected from the Hebrew canon in about AD 90. The collection was included in the Latin translation of the Bible (the Vulgate) and also in the 1611 authorized King James version. As early as 1629 the Puritans demanded that it be removed from the King James version, and in 1827, Protestant Bible societies took a definite stand against it. That was just before the Prophet Joseph Smith inquired of the Lord in 1833 whether the Apocrypha needed to be retranslated, because it was in his Bible (see preface to D&C 91) and was known to be controversial. It is still in the Catholic Bible. To me it is worth reading only after one has read the entire Old Testament, and even then some of the books in it could be skipped entirely.
But what about the Book of Jasher? Is it worth reading? Just how authentic is it? Was it ever included in a collection of canonized books of scripture? Let us now review the history of the Book of Jasher, and then discuss how modern revelation supports its authenticity.
Referenced in Bible. The Bible quotes a Book of Jasher as a reliable source. The Book of Joshua includes the account of a highly unusual event. A miracle of truly grand scale, if understood literally, is the “Long Day of Joshua” where the author of the Book of Joshua states:
And the sun stood still, and the moon stayed, until the people had avenged themselves upon their enemies. Is not this written in the book of Jasher? So the sun stood still in the midst of heaven, and hasted not to go down about a whole day. 
Why does the author state that the account is written in the Book of Jasher? Is it not because the miracle seems so unusual that he needed to give a reference to the source of this information? The real Book of Jasher was so highly regarded as to be quoted as the source of an account of the sun standing still.
The other Biblical reference is to David’s having archery taught to his army:
(Also he bade them teach the children of Judah the use of the bow: behold, it is written in the book of Jasher.)