Most sailed voyages leave from Ushuaia in Argentina, at the southern tip of the continent. Fly cruises leave from Punta Arenas in Chile, where you board the charter flight across to King George Island. Some sailings depart from Puerto Williams instead.
One practical thing that catches people out on fly trips: seats on the Antarctic flight are often allocated first come. If a window seat matters to you, be early.
Which city you fly into shapes your whole pre-trip plan, including how many buffer days to build in. We'd always suggest arriving at least a day ahead of your embarkation, and more if your connections are tight.