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Antarctica is international territory. You can start your own country there.
1. Before the Antarctic Treaty of 1959, seven nations made territorial claims in Antarctica and the sub-Antarctic Islands. Under the Treaty, recognized by 45 countries, 'no new claim, or enlargement of an existing claim, to territorial sovereignty shall be asserted while the present Treaty is in force.' But most nations, even among the signatories, do not recognize the existing claims (for example, the U.S.) or care about new ones. All the same, don't neglect to take a Norwegian with you.
2. Pick your desired general location, bearing in mind the question, Where will I supply myself from? (Claimed territory will likely be better; unclaimed territory will be smoother politically.) There are no claims between 90° W and 150° W, on the Pacific coast.
3. Reconnoiter. Find a suitable harbor, keeping in mind that it may be on an ice shelf, not land. McMurdo (in the New Zealand zone) is Antarctica's only usable harbor for large ships, and for only a few months a year. Rely on small ships and plan on a small colony for a start.
4. Provision. You will need esp. fuel (mining is prohibited de jure and there are no trees) and food (hunting and collecting are prohibited without a permit). Almost all resources will be scarce or off-limits. (U.S. nationals are bound by the Antarctic Conservation Act.) Build with fabric where possible, if space is at a premium, but note you will need steel platforms on stilts for permanent structures. Do not build with ice except in emergencies. This is not the Arctic, and you are trying to be civilized.
5. Land. The end of winter will allow you to take advantage of the all the warmest parts of the year. Oddly, though, the Antarctic summer is not ideal for growing plants, because they respire at night (you've got no night). The warm weather can be good for fishing and exploration.
6. Devise a fisheries infrastructure (fishing is fine) for a small fleet and shoremen. Coordinate waste collection. Set up hydroponic, artificial light greenhouses, bearing in mind to allow at least a season (of course) for things to grow. Meat from domesticated animals may have to be imported for some time as feed will be limited. But when your agricultural product is sufficient, stable herds and graze flocks.
7. Don't forget to keep importing supplies: you don't have any there.
8. Summon the Pope to crown you Emperor.