If you're not a penguin (they swim), airplane is the best way to reach Antarctica. Antarctica is the southern continent, so from anywhere in the USA, you could just go south, and you would eventually reach the Antarctic. But Antarctica is a big place, so just "getting there" doesn't necessarily mean that you've gotten where you need to go.
I'm working in the McMurdo Dry Valleys (77S 162E). If you pull out a globe (okay, or Google Earth--it has some great satellite images) you'll seem that this is nearly due south of New Zealand. If I flew south from Providence, RI, my old home, I'd arrive on the wrong "side" of Antarctica (technically, the wrong coast). The Antarctic Penninsula is fascinating in its own right, but with a land area about the size of the US and Mexico put together, there'd be a lot of Antarctica between me and the Dry Valleys.
So I'm off to Aukland, New Zealand tonight. From there, it's on to Christchurch on the south island. More from NZ (and from "tomorrow"-- I'm about to gain 16 hours of time zone!)