How to make a rogue planet liveable?
Rogue planets are generally not to healthy for us humans to live on. No permanent source of heat or light means that generally they are a pretty cold place. Plenty of other problems arise too, but lets not get into all of that.
How do I make a rogue planet of Earth-like proportions habitable by humans?
My habitants certainly don't need to be strolling around in lush green parks, but I would like them to be able to survive for many centuries.
Assume futuristic technology, limited by incapability to engage in Faster Than Light travel. Also assume that cost is no issue: all of humanity is united in this singular goal.
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The main problem would be energy. Without a star as energy source, you will have to produce all the energy yourself. You'll need a lot of energy, so probably fusion is the right source (note that in the end, stars are also nothing but huge fusion reactors). I'll assume by then humanity has managed controlled fusion of standard hydrogen (as opposed to our current attempts which still need deuterium), so there is no lack of fuel.
The next problem is that without a star to heat the planet, the atmosphere will be frozen (apart from a few local places with geothermal activity). So you'll probably start settling on the surface of the frozen atmosphere, and gradually work down to the surface. This has a big problem: Most of the oxygen is probably below the frozen atmosphere (as that planet would not have life, the atmosphere would not contain oxygen), either bound in water (ice), or bound in rocks. So you'll need to get to the ground before the oxygen supply you brought with you is no longer sufficient (you may need to apply strict population control in order to prevent oxygen needs to grow too fast). I'd build the first power plants as satellites around the planet, so they are not affected by the later melting/boiling of the atmosphere.
But as soon as you have secured access to the planet's actual surface, it's really just a matter of how much energy you can produce. So build enough fusion reactors to keep the atmosphere warm (and produce enough greenhouse gases to keep losses to space low), and split enough water top produce oxygen (you probably have to do that anyway to get the hydrogen for your fusion reactors), and assuming the planet is sufficiently earth-like, the rest should be simple: Plants can grow under artificial light in hydroponic greenhouses (assuming the people of the time actually eat plant matter, not artificially created food). Advanced technology should be able to build all the substances you need using the elements found on the planet and the energy provided by the fusion plants.
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