Translating the Book of Mormon into other languages commenced relatively soon after the first publication in 1830. As of April 2011, the Book of Mormon has been published in its entirety in 82 languages, with selections of the book available in an additional 25 languages. The first edition of the Book of Mormon after English was Danish in 1851, followed by French, Italian, Welsh, and German in 1852.  There was even a Deseret Alphabet version. As far as possible, the translators were to be members of The Church of Jesus Christ of Latter-day Saints, but as the Church expanded rapidly with missionaries entering new countries, it was necessary sometimes to employ translators from outside the Church. Such was the case in South Africa. Currently Afrikaans is the native tongue of about 13% of the population in South Africa. 
John M. Pontius was a missionary for The Church of Jesus Christ of Latter-day Saints in South Africa from 1971–73. He describes the yearning for Afrikaans-speakers for a translation of the Book of Mormon
I attended the special conference in Johannesburg on May 14, 1972 when the new translation of the Book of Mormon into Afrikaans (Die Boek van Mormon) was presented. It was an electric moment. People wept. Some had waited all of their lifetimes to read the Book of Mormon in Afrikaans. Many people had learned English for the sole purpose of reading this scripture. The Spirit was strong among us as we rejoiced. 
But this was not the only remarkable aspect of this conference. John Pontius and a fellow missionary were present on several occasions when the translator, Professor Felix Mynhardt, talked about the translation process. In his blogpost, Pontius recounts their collective recollections, including what Mynhardt said at the conference itself.
Prof. Mynhardt was not a member of the Church of Jesus Christ. Pontius recalls, “He said that he was fluent in over 60 languages. He was presently employed at Pretoria University as a language professor. He said he had been praying that the Lord would give him some task, some divinely important task, that would justify his having this gift of language from God.” He had been approached in 1970 by the Mission President, Harlan Clark and others to translate the Book of Mormon in Afrikaans. Pontius recalls:
He said that he knew of the Book of Mormon from his religion studies, and his initial reaction was that he did not want to be involved in translating it. However, that evening, as he prayed upon his knees, as was his habit, he said the Spirit of the Lord convinced him. The message was something on the order of, “You asked me for a great, divinely inspired task of translation, I sent it to you in the form of translating the Book of Mormon, and you declined.” Professor Mynardt said he could not sleep through the night because he knew that translating the Book of Mormon would get him into trouble with his university, which was owned and operated by the Dutch Reformed Church. When morning came he agreed to begin the translation immediately.
Once Mynhardt began translating, it was obvious that the Book of Mormon had not been written in English. Joseph Smith had therefore translated, not composed it. “It became immediately apparent that what I was reading was a translation into English from some other language. The sentence structure was wrong for native English. The word choices were wrong, as were many phrases.” Working on that assumption, Mynhardt knew he would have to find the original language to be able to make as accurate a translation into Afrikaans as possible. Pontius narrates,
He listed a half-dozen languages he tried, all of which did not accommodate the strange sentence structure found in the Book of Mormon. He said he finally tried Egyptian, and to his complete surprise, he found that the Book of Mormon translated flawlessly into . . . ancient Egyptian. He found that some nouns were missing from Egyptian, so he used Hebrew nouns where Egyptian did not provide the word or phrase. He chose Hebrew because both languages existed in the same place anciently.
Mynhardt had begun translating—illogically—in the middle of the book, so when he turned to the beginning to commence that translation,
Imagine my utter astonishment when . . . [I] came to verse two, where Nephi describes that he was writing in the language of the Egyptians, with the learning of the Jews! . . . I knew by the second verse, that this was no ordinary book, that it was not the writings of Joseph Smith, but that it was of ancient origin. I could have saved myself months of work if I had just begun at the beginning. Nobody but God, working through a prophet of God, in this case Nephi, would have included a statement of the language he was writing in. Consider, how many documents written in English, include the phrase, “I am writing in English!” It is unthinkable and absolute proof of the inspired origins of this book.
Mynhardt said that he was perhaps the only person at that time in South Africa who had the language skills necessary to make the Afrikaans translation, using as he did, ancient Egyptian, Hebrew, Afrikaans, and English. He had this to say about Joseph Smith:
I do not know what Joseph Smith was before he translated this book, and I do not know what he was afterward, but while he translated this book, he was a prophet of God! I know he was a prophet! I testify to you that he was a prophet while he brought forth this book! He could have been nothing else! No person in 1827 could have done what he did.  The science did not exist. The knowledge of ancient Egyptian did not exist. The knowledge of these ancient times and ancient Peoples did not exist. The Book of Mormon is scripture. I hope you realize this. . . . I declare that the Book of Mormon is of ancient origin, and is scripture of the same caliber as the Old Testament, or for that matter, the New Testament.
Pontius concludes his meaningful account by describing the effect on him of this testimony of the ancient origins of the Book of Mormon from someone who was not a member of the Church, “I know my memory of his exact words is wanting, but my memory of what I felt and what I knew and how potent it was to hear his testimony of Joseph Smith and the Book of Mormon is one of those things that I will never forget.”
From a personal standpoint, some time ago I had to edit a piece in English written by a German speaker that was very difficult to understand. The only way I could edit it successfully was by translating it back into German to see the idioms used, and then re-translating it into English. Unless you are a native speaker of both languages, in most cases it is extremely difficult to render an accurate translation. The unique skills that Prof. Mynhardt employed in translating the Book of Mormon into Afrikaans (the translation is still in use today), were in my opinion divine gifts bestowed on him for this particular purpose.
This article was written by Alison Coutts, a member of The Church of Jesus Christ of Latter-day Saints.
3. Unless otherwise noted, information and quotes come from John Pontius’s blogpost
4. As far as is known, the translation process began in 1828.