My knowledge comes from my study of Victorian literature and touches more on the middle class than the upper class, but I hope you will find it useful. :)

Let me answer this with a little background on conversation and its importance in Victorian culture. The rise of industrialization and the creation of a wealthy middle class created a social challenge to the established aristocracy and gentry. Bank owners, industrialists, merchants, investors in foreign markets and trade, etc. now had the capital to adopt many of the trappings of the societal leaders: they bought huge houses in the country, they could keep their own coaches, they could throw big suppers.

Rather than just enjoying the luxuries of the aristocracy, the newly wealthy middle class wanted access to political and social power that had traditionally been in the hands of the aristocrats. They didn't want to just have their own big houses, they wanted to be invited to the original big houses for dinner parties, where they could increase their social capital by making important connections. But, as wealth and possessions no longer made a clear distinction between classes, people started relying increasingly on etiquette. If you wanted to get by, you had to learn how to do as the nobs do. Knowing how to dress, how to behave, etc. became an important marker of one of the upper crust. For example, if you knew which was which among the dizzying array of spoons and forks and things at supper, you could avoid humiliating yourself and "exposing" yourself as not having been born wealthy. An aristocrat would have been taught these rules from birth. But what about the industrious industrialist, who made his money opening a canning factory in Liverpool? He (and his family) would have to learn etiquette as a form of cultural capital. This included learning how to speak.

David Newsome illustrates the importance of speaking well in The Victorian World Picture: "You could not always hope to deceive others and one little slip could let you down. 'The real tyranny' of modern society, [John Stuart] Mill once wrote, 'is the tyranny of your nextdoor neighbour'; the fear of being found out to not really be what you are pretending to be. Trollope gave himself away - according to John Bright - at a dinner-party in 1876, given by Sir Charles Trevalyan. Bright noted in his diary: 'Trollope, the author of many novels, was there. He is rather loud and boisterous in his manner of speaking.' Charles Dickens sometimes, unconsciously, betrayed his origins. ... As the evening wore on, he relaxed. When he was occasionally interrupted by a question, he let fall from his lips a very common expression - 'oh Lord no'. But worse was to come - a genuine cockneyism: 'Oh, lor', no,' he said. It did not pass unnoticed." (76)

This sort of tension can be seen in what were called "fashionable novels" or "silver fork novels." These were marketed as depicting the lives of the aristocracy, and almost always centered on a marriage plot. In reality, they were criticized as being actually written by outsiders from the middle class, serving as a kind of roadmap for how to behave in aristocratic circles.

Knowing how to be charming at a supper was very important: it could the key to being invited back. Oscar Wilde is remembered as being particularly clever, but some journals of people he ate with complain that they had heard him use a particular witticism at a previous dinner. This shows just how formulaic the eloquence of a Victorian could be: bon mots about popular topics were very often prepared ahead of time and then deployed at opportune moments.

Mr. Turveydrop in Bleak House is a wonderful example of a middle class master of etiquette (or Deportment, as it is called in the novel). Demonstrating his obsession with acting like the aristocracy, he names his son Prince and prides himself in knowing how to behave in all situations. He himself is the model of Deportment: he always knows what to say, whom to be deferential to, and how to ingratiate himself with anyone. On the other hand, he is also stone broke, and lives off of his son's income as a dancing instructor.

I once read a book for young ladies published at the beginning of the twentieth century that gave advice on conversation. Apart from simple rules such as not talking too loudly and not hogging attention, it also suggested little witticisms to use if certain subjects are mentioned. Instead of providing a brief overview of the subject, it just gave a stock statement to use if the subject is mentioned. I don't recall the specifics, I'm afraid, but one of them instructed young ladies to say "Oh, (philosopher name)? He's awfully interesting, but I'm afraid I find him to be too cerebral. I much prefer..." and then steering the conversation back into more familiar waters. There was heavy emphasis on always having something to say (even if the result was sometimes inane, and exposed one's own ignorance), to the point that it was frequently satirized. For example, see this cartoon from the satire magazine Punch.

But wait! I hear you say. This is all about the middle class. The question was about the aristocracy. Here I have to say that, at least in my reading, Victorian studies have focused much more on the middle class, so I know much more about the middle-class-aspiring-to-join-the-aristocracy than I do about the aristocracy itself. This may be because the aristocracy were instructed by family, governesses, and tutors, not out of a book, so we do not have as many primary texts to refer to. That being said, the aristocracy was trained from an early age in the Classics (including rhetoric, history, and drama) and received an education that focused very much on speaking at the private schools. Since my knowledge of education in the Victorian period is sparse, I won't attempt to get into it here.