I did a little experiment on lds.org, searching the following words:
fanny alger: 0 hits
sylvia lyon: 0 hits
Helen Mar Kimball: 1 hit, no mention of plural marriage
zina d.h. young: 19 hits, mentions of being Joseph's plural wife: 0
Eliza Partridge: 1 hit
Emily Partridge: 1 hit
A fairly explicit discussion in a 1979 Ensign article:
Emma Smith needed help with her newborn son, and hired first sixteen-year-old Emily, then twenty-year-old Eliza too.
Although little Don Carlos Smith died a short time later, Emily and Eliza continued to live in the Smith home, where, in the summer of 1842, both girls “were married to Bro. Joseph about the same time, but neither of us knew about the other at the time; everything was so secret” (Emily, “Incidents,” p. 186).
louisa beaman: 1 hit, as follows, from the "Church History in the Fulness of Times" manual:
Moreover, Joseph Smith and the Church were to accept the principle of plural marriage as part of the restoration of all things (see v. 45). Accustomed to conventional marriage patterns, the Prophet was at first understandably reluctant to engage in this new practice. Due to a lack of historical documentation, we do not know what his early attempts were to comply with the commandment in Ohio. His first recorded plural marriage in Nauvoo was to Louisa Beaman; it was performed by Bishop Joseph B. Noble on 5 April 1841. 12 During the next three years Joseph took additional plural wives in accordance with the Lord’s commands.
Joseph Smith Plural Marriage: 94 hits
Some representative quotes:
This is the sum total of the discussion of plural marriage in Hinckley's "Truth Restored" (the rest of the section covers the persecution it engendered):
Although polygamy is no longer practiced in the Church, no account of the Church’s history can be complete without some discussion of the practice. It was first announced by Joseph Smith at Nauvoo in 1842. Many of those close to him knew of it and accepted it as a principle of divine pronouncement. However, it was not publicly taught until 1852.
In the families that practiced polygamy, each wife, with her children, occupied a separate house, or, if the wives lived in the same house, as was sometimes the case, in separate quarters. No distinction was made between either of the wives or the children. The husband provided for each family, was responsible for the education of the children, and gave both the children and their mothers the same advantages he would have given to his family under a monogamous relationship. If it was thought he could not do this, he was not permitted to enter into plural marriage.
While the practice was extremely limited—only a small minority of the families were involved—it was the kind of thing of which enemies of the Church could easily take advantage.
A 1977 article from Davis Bitton:
Starting during Joseph Smith’s own lifetime but limited to a few dozen families until its official announcement in 1852, plural marriage brought a powerful new challenge to the equanimity of Latter-day Saint family life.
The church's main page about plural marriage says:
After God revealed the doctrine of plural marriage to Joseph Smith in 1831 and commanded him to live it, the Prophet, over a period of years, cautiously taught the doctrine to some close associates. Eventually, he and a small number of Church leaders entered into plural marriages in the early years of the Church. Those who practiced plural marriage at that time, both male and female, experienced a significant trial of their faith. The practice was so foreign to them that they needed and received personal inspiration from God to help them obey the commandment.
Liahona:
July 12 [1843]. A revelation on the “Eternity of the Marriage Covenant and Plural Marriage” (D&C 132) was recorded, giving fuller meaning to the “new and everlasting covenant” which had been mentioned as early as 1831. The Prophet had explained the doctrine to a few, and plural marriages had been performed in 1841.
Teachings of the Presidents of the Church: Joseph Smith:
This book also does not discuss plural marriage. The doctrines and principles relating to plural marriage were revealed to Joseph Smith as early as 1831. The Prophet taught the doctrine of plural marriage, and a number of such marriages were performed during his lifetime. ...
In 1841 the first sealings of couples were performed, and in 1843 the Prophet dictated the revelation that describes the eternal nature of the marriage covenant (see D&C 132). The doctrines in this revelation had been known by the Prophet since 1831. 21 As commanded by God, he also taught the doctrine of plural marriage.
The only mention in the Gospel Doctrine D&C manual:
The revelation to practice plural marriage in this dispensation
In this dispensation, the Lord commanded some of the early Saints to practice plural marriage. The Prophet Joseph Smith and those closest to him, including Brigham Young and Heber C. Kimball, were challenged by this command, but they obeyed it. Church leaders regulated the practice. Those entering into it had to be authorized to do so, and the marriages had to be performed through the sealing power of the priesthood.
A D. Michael Quinn article from the Ensign in 1978 is unusually frank:
How a family accepts members who join it by marriage is, in some ways, analogous to how a Church accepts members who join it by baptism. The experiences of plural marriage make the analogy even closer. The Whitney family rose nobly to the challenge in a way that was an example to the Church. On 27 July 1842, the Prophet Joseph Smith recorded a revelation to the Whitneys on plural marriage.
“My husband revealed these things to me; we had always been united, and had the utmost faith and confidence in each other. We pondered upon them continually, and our prayers were unceasing that the Lord would grant us some special manifestation concerning this new and strange doctrine. The Lord was very merciful to us; He revealed unto us His power and glory. We were seemingly wrapt in a heavenly vision, a halo of light encircled us, and we were convinced in our own minds that God had heard and answered our prayers and intercedings before Him.” 10 In obedience to the command of the living prophet, Newel and Elizabeth Ann gave their daughter Sarah Ann in marriage to Joseph Smith. Nearly a year later, Joseph Smith dictated the general revelation about the eternity of marriage and the nature of plural marriage, and Newel asked to have his own copy, a providential request, since the first copy was destroyed. Thus, Newel’s desire to have the word of the Lord has blessed the entire Church by preserving what is now Section 132 [D&C 132] in the Doctrine and Covenants.
I could go on, but it seems to me the church was much more forthcoming back in the 1970s and since then has avoided the subject, usually preferring just to say that Joseph taught it to a select group. I am pretty sure I learned Joseph Smith was a polygamist on my mission. We didn't learn about it in seminary, and I wasn't a diligent Ensign reader before then.
If one doesn't read current church publications carefully, one might not know Joseph had more than one wife. It's a good thing we have the interwebs.