the three biggest things in my experience were persistence, recommendations, and proof of hard work.
persistence is easy. apply, apply again, talk to people, call people, work every angle possible and ride that fine line between persistence and annoyance. you need to make yourself standout against a VERY large crowd when applying for the entry-level positions. humor helps – one girl i know who had success mailed homeade postcards to the hiring managers while she was traveling through mexico – goofy reminders of the fact that she was still out there. it got people to remember her and definitely helped to bring her resume out above the many others.
recommendations – if you know anyone who works for the program or has worked for the program and they were successful (i.e. not fired), their recommendation can have a lot of pull.
proof of hard work – ever worked a job that was routinely 60+ hours a week or more? ever worked or lived in a harsh or isolated environment with other people? ever done physical labor at all? honestly, it seems far less about the skill specific to the job (at the entry level) and far more about the hiring manager knowing you won’t run down after 60 hour work weeks in extreme environments. it’s tough, especially at the pole when you have to contend with altitude and a tighter work schedule.
tough, but gratifying in the extreme. good luck!