The authenticity of this and the next dialogue have usually not been questioned, because stylistically they are very closely linked with Laws, Timaeus, and Critias, and there are fairly good reasons for thinking those authentic, especially the Laws. In addition there are statements in Aristotle that seem to be references to the Sophist, although they could also be read other ways (e.g., as claiming that Plato himself made a statement about sophists). Content-wise, however, people have often been uncomfortable with the Sophist and the Statesman, because they are so very different from what one would expect of Plato. As I've said many times before, this in itself means nothing -- all the dialogues do something you wouldn't expect simply from the other dialogues -- but it is true that these dialogues give us something rather different from most other dialogues. Because of this, questions about their inauthenticity occasionally reappear. It has even been argued that they are really by Aristotle, in part because they match up fairly well with comments Aristotle himself makes about his own philosophical dialogues in the Politics. Nice as it would be to discover that two of Aristotle's missing philosophical dialogues were actually hiding in plain sight all this time, I find the arguments to this end rather tenuous, and I take it that Plato scholars do, as well.
You can read the Sophist online in English at the Perseus Project and in French at Wikisource. Mary Louis Gill has an interesting article on Method and Metaphysics in Plato's Sophist and Statesman at the SEP.
The dialogue has the same characters as Theaetetus (Socrates, Theodorus, Theaetetus, Socrates the Younger) and one addition, the Eleatic Stranger (xenos), about whom, of course, we know only that he is a stranger from Elea and that he studied with Parmenides and Zeno.
Theodorus opens the dialogue by telling Socrates that they've come back and brought a visitor from Elea, who is "very much a philosopher" (216a). Socrates remarks that in Homer visitors are sometimes gods in disguise, and the visitor might well be "a god of refutation to keep watch on us and show how bad we are at speaking--and refute us" (216b). Theodorus replies that it isn't the visitor's style and he is only divine in the way all philosophers are. Socrates says in return that philosophers are probably no easier to distinguish from other men than gods are:
Sometimes they take on the appearance of statesman, and sometimes of sophists. Sometimes, too, they might give the impression that they're completely insane. (216c-d)
He asks the Stranger whether they distinguish sophists, statesmen, and philosophers. The Stranger replies that they do, but it isn't easy to do so. They settle on the Stranger teaching the topic by question and answer with the young men, and Theaetetus agrees. They begin the discussion, first giving a practice run with angling before going on to sophistry.
The Stranger makes use of division, but not a strict one, since he allows one thing to fall under different branches of a division, a point which will be essential to the attempt to pin down what a sophist is, who seems to practice both a productive and an acquisitive skill (techne). This shows why the sophist is so hard to define: he is found under different guises or appearances. The Stranger will identify five different guises under which the sophist appears (231d-e):
1. Hired hunter of rich young men.
2. Wholesaler of learning about the soul.
3. Retailer of learning about the soul.
4. Seller of his own learning.
5. Athlete in verbal combat and debate.
In addition, a sixth is mentioned and put into doubt, but is added for the sake of discussion:
6. One who cleanses the soul of beliefs interfering with learning.
None of these guises is actually put forward as a definition. Rather, the Stranger is weaving a net of descriptions (235b) to hunt down the sophist by hemming him in from several different sides. They then discuss the way in which the sophist is an imitator, since the sophist could not possibly know everything he purports to teach; he is a copy-maker, but someone who produces false copies. But this raises the question of falsity, and how anyone can speak falsely at all; a question that the Stranger answers by arguing against Parmenides. This is necessary, because the fundamental principle of Parmenidean metaphysis is 'that which is, is, and that which is not, is not'; but the sophist uses an interweaving of that which is and that which is not to mix the two. In order to capture the sophist, we need to have a proper account of falsehood, one that Parmenides cannot provide.
When we look at accounts of that which is and that which is not, we find "something like a battle of gods and giants" (246a). One side insists that being must be given an account entirely in terms of what can be sensed, what is bodily; the other insists that certain noncorporeal forms can be thought of and that these alone truly are. But, the Stranger says, neither side can be right if philosophy is to exist at all:
The philosopher--the person who values these things the most--absolutely has to refuse to accept the claim that everything is at rest, either from defenders of the one or from friends of the many forms. In addition he has to refuse to listen to people who say that that which is changes in every way. He has to be like a child begging for "both," and say that that which is--everything--is both the changing and the unchanging (249c-d)
This requires dialectic, the process of being able to make distinctions; and making distinctions requires attention to the five forms of being: change, rest, same, different, and that which is. This leads the Stranger to argue that 'that which is not' in some way is -- it is not inconsistent with that which is but something different. Thus, for instance, to distinguish the beautiful from the non-beautiful is really to set being over against being. Negation always presupposes being. This allows one to give an account of the sophists, who deal with mere copies, appearances.
And the dialogue ends with the Stranger's definition of sophistry, and Theaetetus' agreement with it:
Imitation of the contrary-speech-producing, insincere and unknowing sort, of the appearance-making kind of copy-making the word-juggling part of production that's marked off as human and not divine. (268c)
That is, the sophist is a producer of mere appearances on the basis of mere opinion, using words to force people to contradict themselves.
* The trilogy of dialogues has a theme of appearances and copies and imitations, and that extends even to the characters: Theaetetus is like Socrates in appearance; Socrates the Younger, who will speak in the next dialogue and is said in this one to be Theaetetus' substitute or stand-in, shares Socrates' name but is not Socrates; the sophist seems to be like a philosopher but is not; Socrates seems to be like a sophist and yet is not; and so forth.
* The Stranger's being from Elea is of course significant. Theaetetus had laid out the opposition between the fluent philosophers, represented by Heraclitus, and the steadfast philosophers, represented by Parmenides; it then criticized the former and sophists like Protagoras as being of the same family. Cratylus continued the criticism of the fluent philosophers by examining implicit assumptions of Greek culture (as represented in Greek language and literature) that were allied to the fluent philosophy. With the Eleatic Stranger we get an examination of the other side of the opposition. (It is notable that there seems to be a direct reference at 216c to Socrates' own discussion with Parmenides in Parmenides.) Elea, a Greek colony in Italy, was the home of the two major Eleatic philosophers, Parmenides and Zeno, so he is, so to speak, in the know when it comes to their philosophy -- Theodorus introduces him as a follower of them, and he quotes Parmenides' poem-treatise -- and can thus serve as an informed critic of their position.
The crux of the criticism of the Parmenidean position, interestingly, is its inability to account for the sophists, and thus its inability to demarcate dangerous sophists from beneficial philosophers; an important matter as we approach Socrates' trial.
* The Stranger's account of how they will proceed at 218b-c fits very well with what the Cratylus suggested would be required:
But with me I think you need to begin the investigation from the sophist--by searching for him and giving a clear account[logou] of what he is. Now in this case you and I only have the name in common, and maybe we've each used it for a different thing. In every case, though, we always need to be in agreement abut the thing itself by means of a verbal explanation [dia logon], rather than doing without any such explanation [choris logou] and merely agreeing about the name.
However, this could also suggest the last part of Theaetetus, about how true judgment with logos is not knowledge; it at least raises the question whether we will get anything from the Stranger beyond true judgment with logos.
* The description of the sixth guise is worth noting, since it sounds remarkably like Socrates (230b-d):
They cross-examine someone when he thinks he's saying something though he's saying nothing. Then, since his opinions will vary inconsistently, these people will easily scrutinize them. They collect his opinions together during the discussion, put them side by side, and show that they conflict with each other at the same time on the same subjects in relation to the same things and in the same respects. The people who are being examined see this, get angry at themselves, and become calmer toward others. They lose their inflated and rigid beliefs about themselves that way, and no loss is pleasanter to hear or has a more lasting effect on them. Doctors who work on the body think it can't benefit from any food that's people who cleanse the soul, my young friend, likewise think the soul, too, won't get any advantage from any learning that's offered to it until someone shames it by refuting it, removes the opinions that interfere with learning, and exhibits it cleansed, believing it knows only those things that it does know, and nothing more.
This should be compared with Socrates' comments to Theaetetus at the very end of Theaetetus.
* There is no consensus on how the overall dialogue should be interpreted, in part because Socrates is quiet for most of the discussion. Some commentators see the Stranger and Socrates as being in fundamental agreement: Socrates 'noble sophistry' contrasts with sophistry in the proper sense. Others see the final definition of the sophist as an implicit attack on Socrates, an attack continued in the Statesman. One example of the latter is Catherine Zuckert in Plato's Philosophers:
If the Eleatic is an exemplar of the dialectical science and thus of philosophy, as he suggests, then in his judgment Socrates cannot be a philosopher, even though the Eleatic is too urbane to say so explicitly. He contents himself with intimating that Socrates is a sophist who imitates a knower by refuting his interlocutors in private conversations, even though he himself is perfectly and ironically aware that he does not know. (p. 706)
If this is true, the Eleatic Stranger is setting up a set of challenges to which Socrates must respond at his trial and in his final days: to show that he is a philosopher and not a sophist.
Quotations from Sophist are from Nicholas P. White's translation in Plato, Complete Works, Cooper & Hutchinson, eds., pp. 235-293.