[sbierwagen]

Larry Niven, "Bigger Than Worlds" (1974)

  ...assuming that the galaxy's most advanced civilizations are protoplasmic. But 
  beings whose chemistry is based on molten copper, say, would want a hotter 
  environment. They might have evolved faster, in temperatures where chemistry and 
  biochemistry would move far faster. There might be a lot more of them than of 
  us. And their red-hot Dyson spheres would look deceptively like red giant or 
  supergiant stars. One wonders.

[mediocregopher]

Speaking of Larry Niven, my impression after reading Ringworld (in addition to "holy shit that was good") was that Dyson Spheres were kind of a non-workable, and that a species who'd advanced far enough to actually make one could probably just colonize another system anyway.

[sbierwagen]

A swarm-Dyson sphere, which is the only kind that can be realistically built, is incremental. You just keep building habitats in orbit around the sun, until eventually you capture all the sunlight.

[nitrogen]

Clearly a solid Dyson sphere is not orbiting its host star, and could eventually drift into the star. However, might it be possible to harvest enough energy from the star to power a propulsion system that keeps the sphere in place?

[technolem]

Won't gravity stop this from happening? Seriously, the shell of the sphere will be balanced on the outskirts of a gravity well right? So if it moves this will move the center of the gravity well and both the star and sphere should fall back towards the center.

[nitrogen]

According to Newtonian gravity, an object inside a sphere experiences zero net gravity from the sphere, and vice versa.

http://en.wikipedia.org/wiki/Dyson_sphere#Dyson_shell