When you attack a base you can occupy it by clicking the "attack and occupy" option. When you click this you will occupy the base if your attacking force can destroy the defending forces. When you finish the attack the debris created by the destroyed ships will be displayed and it can be harvested by any Recyclers which visit the base. You can Pillage the base daily (a minimum of 24 hours between pillage operations). While you occupy a base 30% of it's hourly economy goes to you! The base also suffers an additional 30% reduction to its construction and research ratings, and a 50% reduction to of its production.