See The Sophists : Protagoras :
Plato [in Meno, 91e] says that he [Protagoras] practised as a sophist for over forty years till his death at about seventy (probably about 420 BC). In the Protagoras he also says (316d–317b) that while the activity of sophistry has been practised by poets and other experts from ancient times, he is the first person to have openly proclaimed himself a “sophist” and claimed to teach people (sc. how to achieve success in life); he thus claims for himself recognition of his professional status in a role, that of teacher of human excellence as a means to success in life, which was traditionally claimed by the poets.
Specifically, in the Protagoras he claims to teach ‘the proper management of one's own affairs, how best to run one's household, and the management of public affairs, how to make the most effective contribution to the affairs of the city by word and action’, and he accepts Socrates' account of that subject as ‘the art of running a city’, which he promises will ‘make men into good citizens’ (319a).
In any event, we do have some evidence for Protagoras' teaching of techniques of argument. Diogenes Laertius' list of titles includes one, ‘The Technique of Eristics’ (Technē Eristikōn) which certainly designates a handbook of argumentative techniques, and another which probably does. The literal title is ‘On Wrestling’, but it is more likely that the wrestling in question is intellectual than physical; there is nothing in our other evidence to suggest that Protagoras set himself up as an athletic coach. (It is relevant that Protagoras' celebrated work ‘Truth’, which began with the famous ‘Man the Measure’ sentence apparently had the alternative title ‘Overthrowing’ (sc. Arguments) (Kataballontes).) So Protagoras taught argumentative strategies, but we have comparatively little evidence of what these actually were.
And see Protagoras :
Protagoras was probably the first Greek to earn money in higher education and he was notorious for the extremely high fees he charged. His teaching included such general areas as public speaking, criticism of poetry, citizenship, and grammar. His teaching methods seemed to consist primarily of lectures, including model orations, analyses of poems, discussions of the meanings and correct uses of words, and general rules of oratory. His audience consisted mainly of wealthy men, from Athens' social and commercial elites. The reason for his popularity among this class had to do with specific characteristics of the Athenian legal system.
In conclusion, it is necessary to make a clear distinction with the current use of "sophistry" as meaning "fallacious" and the original Sophist school or movement, whose main "tools" were rethoric and teaching.
For Plato's critique, see Protagoras (dialogue).
See also Theaetetus, 152a for reference to Protagoras' well-known Man-Measure dictum :
he has said the same thing in a different way. For he says somewhere that man is “the measure of all things, of the existence of the things that are and the non-existence of the things that are not.”
Protagoras' relativism and subjectivism is clearly unacceptable for Plato and his search for definitions :
When Socrates asks a question such as “What is reverence?” he has in mind a question that can be answered only in certain ways. To begin with, he will not be satisfied with an answer that points only to a certain kind of reverence, or only to an example of reverence. The answer must identify a feature that (1) belongs to every kind of reverence (generality requirement), and (2) to nothing that is not reverent (exclusion requirement), and (3) has explanatory power.
And see : Marina McCoy, Plato on the Rhetoric of Philosophers and Sophists (2007), page 3 :
In this book, I examine the distinction between the philosopher and
the sophist in six of Plato’s dialogues, with particular attention to the differences between philosophical and sophistical rhetoric. My argument
focuses on three interrelated theses. First, I argue that Plato’s treatment
of Socrates in conversation with sophists and rhetoricians indicates that
he thought that the distinction between philosopher and sophist was
difficult to make. There is no single method or mode of discourse that
separates the philosopher from the sophist [emphasis added]. One cannot simply say that the philosopher is logical while the sophist is illogical, that the philosopher uses pure reason with no attention to rhetoric while the sophist
persuades apart from reason, or that the philosopher has a successful
method of speaking while the sophist lacks one. Nor are the sophists consistently
presented as disinterested in knowledge or as morally corrupt.
The meanings of the terms philosopher and sophist are disputed at the time
that Plato is writing; for Plato, the claim that Socrates is a philosopher
rather than a sophist is a normative rather than merely a descriptive claim.