RP accent, preferably the Queen's English. Knowing what cutlery to use and how to use it. Extensive understanding of wine and what food goes best with what wine; knowledge of kitchen implements even if they don't use them themselves. Knowledge of art, music, literature, history that they've picked up by osmosis (actually often a private school education). Very well travelled. Well groomed, usually, unless they tend towards the "utterly scruffy aristo jolly buffoon" stereotype.
With the exception of a certain subset (Bullingdon types), lots of posh people don't act too brashly in public or draw attention to themselves, at least in much of England, they're relatively low key.
Degree in something like comparative literature or art history (especially suitable for "gels", as Miss Jean Brodie would have said) or law or PPE (mainly but not only males). Knowing what brands to wear. (The Captain Samuel Vimes 'Boots' theory comes into play here.)
Would probably be like a fish out of water in a Wetherspoons or a rough nightclub (with or without a rotating dancefloor with sticky floorboards) or a disadvantaged neighbourhood (unless they were into ethnography or working for a charity, possibly).
More likely to read (or work for) The Tatler, Horse and Hound, and Wanderlust (and a few others) than Hello and OK. More likely to read The Guardian, Independent, Times, and FT; may or may not read the Daily Mail or Telegraph.
Posh is different from monied although in practice the two often go hand in hand. And then, just to add to the fun, you have all the regional and national variations - "posh" in Ireland, say, is a bit different than "posh" in the south of England. (Yes, I've lived in both. And like a previous poster, I've met and worked with lovely "posh" people and I've also met and worked with some pretty 'orrible ones.)