The Wikipedia Stub gives us the highlighted answers below. They aren't fantastically detailed but essentially accurate. The Hyperion Cantos by Dan Simmons is one of my most favored space operas of all time.
Who are the Ousters?
- In Dan Simmons' Hyperion universe, Ousters are the branch of humanity that left the Worldweb and the Hegemony, and chose instead to travel among the stars, adapting away from planetary life and the influence of the TechnoCore.
Why are they at odds with the Hegemony?
From time to time, the Ousters clash with the Hegemony at the edges of Hegemony space, and are generally considered to be the Hegemony's "prime bogeymen" and "interstellar barbarians".
In truth, the Ousters are extremely civilized and have evolved far beyond the scope of the Hegemony's imagining. They possess superior technology and their "comet forts and can cities" actually resemble pristine old-Earth countryside, replete with waterfalls, fields, giant tree cities, etc.
Where do they live? Why aren't they friendly to the technocore?
- The Ousters have twelve 'swarms', or migration clusters consisting of thousands of ships ranging from single-person to massive habitation structures. Many Ousters live outside of the swarms, though, instead cultivating orbital forest rings around distant stars.
- The Ousters loathe the TechnoCore and refuse to make use of Farcasters, instead relying upon the Hawking drive for interstellar travel.
What makes them unique and opposed to the Hegemony's sensibilities?
- The Ousters have a strong ecological sensibility. Their society has learned the lessons of the destruction of Old Earth, and decided that terraforming is the wrong path. Rather than altering existing planets to suit humans, the Ousters alter themselves to fit the environment. Thus the Ousters come in a huge variety of appearances and forms.
You can look at the Ousters as a Green Movement rather than the Technocore, which is more of a conservative, technological movement. Unfortunately, both are extremes which puts them and their adherents at odds.
While the Technocore created advanced technologies including the fatline and the farcaster using the "Void that Binds" or a form of Planck Space connection between all things, the Ousters wanted nothing to do with those technologies once manipulated by the Technocore.
It is not explained how the Ousters come to understand the evils of the Technocore and its use of "The Void that Binds" to manipulate human beings, tapping into their brainpower for their own uses whenever a farcaster was being used to move between worlds.