It's pretty simple. Takeovers are successful if your military equals or exceeds your opponents military PLUS the strength of the world you want to take.
Temporary and specialized military is included IF applicable to the chosen world.
Vulnerability is simple -- There is a Imperium development that lets you take worlds from a "Rebel" tableau, a Revel development that lets you take worlds from an "Imperium" tableau, and a one-shot development that lets you take worlds from anyone with positive military.
All the details about play order and invoking temporary military more than once are just details to avoid confusion. In most cases, they won't even really apply.
The bit about the cubes and tracks is really more of a reference. It's not strictly necessary, as it only tracks: a.) whether a player has Rebel worlds b.) whether a player has Imperium cards c.) how much "generic" military and how much "Rebel" military they have.
This is all stuff you can figure out by looking at their tableau. The cubes just make it slightly easier.