I think that your demands of greater clarity are fair, but replacing capitalism with something else is something very complicated, so my answer will be unavoidably incomplete and flawed.
Removing the rich people is something that has been attempted in the past and in many occasions succeeded. The secret I'd say is to have at least part of the military in your side. 1917 revolution, Paris commune, Burkina Faso, etc...all share this trait.
@MxVerda @sjuvonen @tinker
The tricky part seems to be twofold. First you need to avoid other powers that are friendly to the rich you have removed that will try do destroy you. This has also happened in failed revolutions like in Germany, Spain or the rest of the springtime of peoples. We could even consider the Napoleonic wars against the French revolution an instance of this. The only solution I see to this is again having the support of the military.