This thread has been superceded as Raytheon are no longer responisble for NSF recruitment in Antarctica, Lockheed Martin instead now fulfilling this function. New thread here:
If you're a US citizen and want to work in Antarctica, the one thing you can do to boost your chances more than anything is to attend one of the job fairs for potential employees.
The main thing to do if you go is to meet the people who go to Antarctica and do the hiring, get emails and phone numbers, get business cards and make yourself known. Take several copies of your resume with you if you go.
Here's a really useful post
for US citizens from a guy who has wintered several times in Antarctica at McMurdo and also the South Pole station.
Raytheon Polar Services Job Fairs