Short Answer: Over the course of 7 years by a committee of Apostles, Oxford Scholars, professional editors, computer experts, and many other contributers form both inside and outside the Church.
What we have for footnotes in the standard works today is the result of many lifetimes worth of diligent scripture study, and thousands of hours work completed as part of a huge effort led by the apostles Thomas S. Monson, Boyd K. Packer, and Bruce R. McConkie, Bruce R. McConkie being a very prominent contributor, having established himself as a student of scripture. In addition to writing the chapter headings, the topical guide, and the bible dictionary, he also produced many of his own footnotes (In the OT alone he produced 600 footnotes that just reference text from the JST, and produced the "Selections from the Joseph Smith Translation" for the references that were too long for the footnotes.)
The work began in 1972 with the creation of the Bible Aids committee, presided by then Elder Thomas S. Monson. The presidency of the Church wanted to publish an LDS version of the KJV Bible, previously the church had used the Oxford
edition of the bible in combination with LDS lesson manuals.
The work they completed is daunting, much came from study, but a significant number of footnotes were the result of custom written programs by Stephen Howes of BYU.
Those of us who witnessed the progress of the project often commented
how individuals in and out of the Church with needed skills and
abilities were available at our time of need. For example, as the work
progressed and it became necessary to process the manuscripts, a
qualified editor, Eleanor Knowles, was available at Deseret Book.
Furthermore, the project could not have been accomplished without the
benefit of modern computer technology; and here again, both in the
people available and in the development of technology, our needs were
met. In anticipation of another project, Eldin Ricks at BYU had placed
every verse of all four standard works into a computer data base. When
it became desirable to have such a data base for the scriptures
project, Brother Ricks willingly let the Church use his material,
saving us thousands of hours.
– Wm. James Mortimer
My former Mission President, Joseph Cook–who was actually mentioned in a talk at the most recent General Conference by his brother Quentin–wrote footnotes into is journals, and would reference them while answering any questions we, his missionaries, may have during personal interviews, it was amazing. I only wish I could see Bruce R. McConkie's personal study journals, but I have a feeling that the vast majority of the fruits of his labours are currently published in the standard works as the study helps, everything else is likely contained in his book, "Mormon Doctrine".
As Brother Mortimer witnesses in the quote above, the work was nowhere short of a miracle when it came to meeting the needs of the project.
History of LDS Scriptures
Harold B. Lee Library. Bible: LDS Publication of the Bible
The Coming Forth of the LDS Editions of Scripture