When we think of what it means to translate, we think of a person who knows two languages and can express the meaning of one language in the other. The translator sees or hears the words of one language and, having facility in both that language and a second, recreates the meaning in the second.
When people speak of Joseph Smith translating the Book of Mormon or the Book of Abraham, they often have that definition in mind and, based on it, either try to corroborate or criticize Smith's work. But he doesn't appear to have translated in the way we usually understand translation. For one thing, he didn't know the first language, even if, trying to uncover the language of Adam, he worked at figuring out Egyptian. So, if we use the ordinary understanding of the word translate, we'll misunderstand what Joseph Smith claimed to have done.
A glance at Webster's 1828 dictionary of American English helps us understand better why Smith called what he did translation. There we see that not until the sixth definition do we get "to interpret." The first four definitions are all variations on "to move from one place to another," and the fifth definition is "to change." If we understand the first four definitions of the word in terms of transmission, we see how Smith understood what he was doing: he was transmitting an ancient text.
There are several accounts of his translation of the Book of Mormon. (See Stephen D. Ricks's article on Book of Mormon translation for a fuller discussion of these.) None of them are cases in which Smith looked at a text and then wrote down the meaning of that text in English. In other words, none of them describe what we would usually think of as translation.
Further, all of the accounts of Smith's translation of the Book of Mormon show him depending on unusual instruments for that work. For example, he used a seer stone placed in a hat to keep out the light, making it easier to see what appeared on the stone. Bizarre behavior to a 21st-century mind, much less bizarre for someone in the early 19th.
Some describe the translation process as one in which Smith saw English words or sentences on the instrument he was using. Another contemporary speaks of Smith translating by means of "spiritual impressions" given by the Holy Ghost. In either case (and the two are not mutually exclusive), he dictated his translation to a scribe, one time through.
There are accounts that suggest Smith used the plates themselves in some way while translating, but his spouse, Emma, says that while she was transcribing for him, the plates lay nearby on the table, wrapped in a linen cloth. At least while she was the transcriptionist, he translated the plates without looking at them. Perhaps he worked one way sometimes and a different way other times, just as he seems to have used different instruments for translation at different times when translating the Book of Mormon.
Evidently some of his contemporaries understood the translation to be both revealed by God and also a product of the time and culture to which it was revealed. A later president of the LDS Church and a close acquaintance of Joseph Smith, Brigham Young, said, “I will even venture to say that if the Book of Mormon were now to be rewritten, in many instances it would materially differ from the present translation” (Journal of Discourses 9:311).
Joseph Smith's later editing of the manuscript suggests as well that his first translation was not given word-for-word by God. (For a comprehensive discussion of that issue, see Royal Skousen.)
Once Smith completed the Book of Mormon he appears no longer to have needed a seer stone or something comparable for his translations. But, interestingly, he continued always to need a physical artifact as a prompt for his translation work, even if (as with the Book of Mormon), he did not actually look at the artifact. (See Terryl Givens, By the Hand of Mormon 177-78.)
Besides the plates of the Book of Mormon, for the Book of Abraham the artifact was an Egyptian scroll that others purchased for him from a traveling showman (Samuel Brown, "Joseph (Smith) in Egypt," Church History 78:1, 26-65; cf. 26). In the case of the Book of Moses, the artifact was the Smith family Bible. Reading that Bible, he dictated the Book of Moses as a text to take the place of Genesis 1-5 (or perhaps as a text parallel to that text).