What do you need to operate a 240V appliance from a 120V socket?

You need the other phase, and a new outlet. Answer Completely new wiring and a different type receptacle. 10/3 cable will be required which isn't exactly cheap. For a short run though....maybe $20 for a scrap piece. Answer Not to mention a new breaker is needed.

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Given that the question states "an" appliance - just one not a house-full - you don't have to go through all that rigmarole. You could use just a step-up transformer plugged into the wall socket - but ensure the earth continuity (unless using double-insulated appliances), power rating, and obviously connector types, are suitable.

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The heading photograph, incidentally, is of the UK pattern, 230V (used to be 240V) a.c. "mains" plug and switched-socket. The large, un-shrouded pin is the earth and also opens a simple mechanical safety-gate within the socket to give the live and neutral pins access to their receptacles. The gate was introduced to guard against the risk of children poking things into sockets!