The bad news is that the UK currently claims (but doesn't use) the habitable part of Antartica. Marie Byrd land is.... inhospitable, to say the least.
When it comes to the hows
, it's relatively simple: You'd set up a research center in the habitable part of Antartica, Brits be damned. It would be possible to exploit the loophole that Britain is not to interfere with science being done in there (and they lack the enforcement ability to do so anyway). Furthermore, it would be possible to actually swindle
scientific agencies of the world to fund expeditions.
Expanding the research station and prolonging the experiments for decades
(adding new ones) would create a de facto population in there. Once that was achieved, there'd be a brief struggle for independence: Hold elections, UDI, that kind of jazz. Since the Brits have no
inhabitants, and the colonists would
, it's more likely than not that the settlers would retain control over the territory, or at least achieve some sort of mutual non-interference deal.
The Antartic coast isn't that different from Greenland: It's shitty and permafrosty, and it's damn cold... But it's survivable with adequate insulation. There's fishery to live off of. Small-scalle greenhouses could be set up. As long as they're properly insulated, there's no reason why they wouldn't work. You don't need to worry that much about equipment overheating: Hell, the place was built
for datacenters. Power would be a bit tricky: However, the antartic glacier looks designed
for large-scale windpower.
It's not been drilled extensively, there's probably lots of untapped fuel to exploit, too.
You exist because we allow it and you will end because we demand it.