There have been many translations of this text, only some of them referenced below. Here is the one given by Lichtheim in "Ancient Egyptian Literature" vol. I, p.59-60:
The respectful man prospers, Praised is the modest one, The tent is open to the silent, The seat of the quiet is spacious. Do not chatter! Knives are sharp against the blunderer. Without hurry except when he faults. When you sit with company, Shun the food you love; Restraint is a brief moment, Gluttony is base and is reproved. A cup of water quenches thirst, A mouthful of herbs strengthens the heart; One good thing stands for goodness, A little something stands for much. Vile is he whose belly covets when (meal)-time has passed, He forgets those in whose house his belly roams. When you sit with a glutton, Eat when his greed has passed; When you drink with a drunkard, Take when his heart is content. Don't fall upon meat by the side of a glutton, Take when he gives you, don't refuse it, Then it will soothe. He who is blameless in matters of food, No word can prevail against him; rHe who is gentle, even timid, The harsh is kinder to him than to his mother, All people are his servants. Let your name go forth While your mouth is silent. When you are summoned, don't boast of strength Among those your age, lest you be opposed. One knows not what may happen, What god does when he punishes.The vizier had his children summoned, after he had understood the ways of men, their character, having become clear to him.' Then he said to them: "All that is written in this book, heed it as I said it. Do not go beyond what has been set down." Then they placed themselves on their bellies. They recited it as it was written. It seemed good to them beyond anything in the whole land. They stood and sat accordingly. Then the majesty of King Huni died; the majesty of King Snefru was raised up as beneficent king in this whole land. Then Kagemni was made mayor of the city and vizier. Colophon: It is finished.
The papyrus itself dates most probably from the twelfth dynasty Egyptian Middle Kingdom, not earlier than the Eleventh Dynasty. It was obtained by the French orientalist Émile Prisse d'Avennes at Thebes in 1847 and is now in the Bibliothèque nationale de France in Paris.
This papyrus has been described by various authors as "the oldest book of the world". For example, Battiscombe G. Gunn describes it 1906 in the following words: "But, as touching the books here translated—the Instructions of Ptah-hotep and of Ke'gemni—they possess, apart from the curious nature of their contents, a feature of the greatest interest, and an adequate claim on the notice of all persons interested in literature and its history. For if the datings and ascriptions in them be accepted as trustworthy (there is no reason why they should not be so accepted), they were composed about four thousand years before Christ, and three thousand five hundred and fifty years before Christ, respectively. And the significance of those remote dates is, that they are the oldest books in the world, the earliest extant specimens of the literary art. They stand on the extreme horizon of all that ocean of paper and ink that has become to us as an atmosphere, a fifth element, an essential of life." (Gunn 1906, p.)
But even if one does not care much about the place in the list of the oldest book in the world, the question about the author and the time of writing seems interesting.
I would say that one can distinguish three theories here. The first one is the one which takes the description given in the text at face value. The kings mentioned at the end of the text are well-known: Huni is the last king of the Third Dynasty, and Snefru the first of the Fourth Dynasty. There was no known visier at that time named Kagemni. But so what? Once the kings themself are well-known, it remains to use the time of their reign, or what the actual scientific mainstream thinks about this. The above quote of Gunn can be taken as an example.
Actually, this theory seems not very popular today, given that there are arguments against such an early time of writing. Lichtheim argues: "When upholding the genuineness of the attributions, scholars are compelled to assume that ... Kagemni and Ptahhotep ... were largely rewritten before they attained the forms in which they were copied in the Middle Kingdom papyri that preserved them, for the language of Kagemni and Ptahhotep is Middle Egyptian, the language of the Middle Kingdom.
The assumption of major alterations in the course of the transmission of the works is, however, a difficult one. There is nothing in our experience with the transmission of Egyptian texts which parallels the assumed translation of Old Egyptian works into Middle Egyptian. Furthermore, the attribution at the end of Kagemni is palpably fictional, for the character of the work is so much more evolved than that of the Instruction of Hardjedef that an attribution that makes it precede Hardjedef by two generations is impossible.
I personally am convinced that all ... Instructions should be classed as pseudepigrapha." (Lichtheim 1973, p.6).
In this case, what would be the alternative? "Once freed from the need to see in them compositions of the Fourth and Fifth Dynasties gready altered by succeeding generations, one can inquire into the probable dates of their composition through the examination of all their aspects: language, style, method of composition, and the kind of thinking they reveal.
Kagemni and Ptahhotep, which stylistically belong closely together, have the loquacity of Sixth Dynasty monumental inscriptions, and in all respects fit into the ambiance of the late Old Kingdom. They reflect a kingship which, whether or not still all powerful, is still serene, and a society that is orderly and optimistic. The nation is in harmony with itself and with the universe; and the moral values taught are the very same that are claimed in the autobiographies.
If seen as belonging to a time near the end of the Old Kingdom, the Middle Egyptian of Ptahhotep and Kagemni is explained as resulting from only minor alterations, for the end of the Sixth Dynasty and the beginning of the Eleventh are only a hundred years apart, and many of the forms characteristic of Middle Egyptian are found in the biographical inscriptions from Sixth Dynasty tombs." (Lichtheim, p.6-7).
But, last but not least, there is yet another possibility of attribution: There is a visier named Kagemni , whose tomb is located at Saqqara, from the early Sixth Dynasty.
This identification is clearly incompatible with the first theory, as was already clear to "A fine tomb of a certain Ke'gemni exists at Memphis; his titles, so far as can be ascertained, are: Judge of the High Court: Governor of the Land unto its Limit, South and North: Director of every Command. He has sometimes been supposed to be identical with our Ke'gemni; but I am assured by those most competent to judge that this tomb cannot be earlier than the Fifth Dynasty (a good three hundred years from the date assigned to the moralist), so that the theory that they are one person may be dismissed as highly improbable. No other person of the name is known." (Gunn 1906, p.16).
But this first theory seems not viable anyway. What about the compatibility with the second theory? Certainly, there is a minor difference: Lichtheim summarizes that "The most plausible date for Kagemni and Ptahhotep [is] the latter part of the Sixth Dynasty." (Lichtheim, p.58), while the Kagemni of the Saqqara tomb is attributed to the beginning of the Sixth Dynasty. But this is only a difference of at most 160 years, thus, probably not a decisive difference in comparison with the additional ~300 years one would have to add for the first theory. Thus, this seems to be a viable theory, and compatible with the so far I consider it as viable. In this case, the epigraph would be partially correct, but the time when Kagemni has lived would have been wrongly attributed in the text.
This theory is, for example, considered by Brunner as highly probable: "Aus der in die Lehre genannten Zeit, den Regierungen des Königs Snofru, ist ein Wesir mit Namen Kagemni nicht bekannt, dagegen existiert in Saqqara das Grab eines solchen aus der frühen 6.Dynastie, und es ist sehr wahrscheinlich, dass dieser Mann mit dem Empfänger der Lehre gemeint ist, zumal sich am Grab Spuren seiner Verehrung gefunden haben. Die Lehre wäre dann, wie manche ägyptischen Literaturwerke, in eine berühmde Vergangenheit zurückdatiert worden. Dass sie noch im Alten Reich, wenn auch gegen dessen Ende, verfasst worden ist, dürfen wir nach Inhalt und Sprache annehmen." (Brunner 1991, p.133).