Good Economist article about Anonymous, their ad-hoc nature and their methods of taking down web sites via DDOS.
Anonymous does not have a typical hierarchical government, but each mission does have a self-appointed dedicated organising body. This organizing body begins the process of setting up the necessary infrastructure, recruiting new members, researching/identifying vulnerable targets, media outreach, and more. However, the organizing body is free to change (and has changed) as the mission evolves day to day. I have observed at least one takeover when the greater group was not happy about what the organisers were doing.