For example, was it a centrally organized system or independent units? Did people at the top (like Hitler himself) give general direction or were they left to improvise on their own etc.?
Centralisation of power and a massive, well-orchestrated bureaucracy were hallmarks of the Nazi regime. The Holocaust was no exception.
Antisemitism was Nazi policy dating back to the party's earliest days, and was a consistent feature of Nazi government from the moment they took office, but the development of the policy underpinning the Holocaust (the 'Final Solution' and extermination as state policy) came together at a 90-minute meeting in January 1942: the Wannsee Conference.
The meeting at Wannsee was intended to coordinate the implementation of the Final Solution across government departments. Present at the meeting were officials from:
The Holocaust was a colossal state effort which involved official institutions at all levels of German society. But the SS — and specifically the RSHA — was the coordinating agency: Himmler was the Final Solution's primary policy architect, and Reinhard Heydrich oversaw its initial implementation. It was Heydrich, in his capacity as the then-head of the RHSA, who called and chaired the meeting at Wannsee.
RSHA was an immensely powerful organisation: a prominent part of Himmler's power-base, it unified under SS control most of the Reich's security and intelligence services. The Gestapo, SD and Kripo (criminal police) were all under its jurisdiction — as were the military units (Totenkopfverbände) which administered and guarded the concentration camps.
The only major intelligence/security force not under RSHA control was the Abwehr (military intelligence) — and most of its functions were handed over to RSHA in 1944 when the Abwehr was dissolved. The logic behind such dramatic centralisation of internal security affairs was to ensure that those forces were ideologically sound — and in the event, the Abwehr was abolished in the aftermath of the July Plot, in large part because its chief, Wilhelm Canaris, was arrested and later executed for his involvement with the anti-Nazi resistance.
The prevailing objective of the SS was not just to ensure the stability and continuity of the Nazi regime, but to enforce its ideology across all aspects of state policy and public life. That is, in large part, why responsibility for overseeing genocide rested in the hands of Himmler and the SS.
The historiography on the Holocaust is huge and extremely well-developed, so you can find plenty of recommended reading elsewhere — if in doubt, Yehuda Bauer is a solid place to start. The minutes of the Wannsee conference make for chillingly euphemistic reading. On the SS and their role in the Holocaust and the Nazi state more broadly (which might be particularly relevant to your question), I'd suggest looking at Heinz Höhne's The Order of the Death's Head or Michael Wildt's An Uncompromising Generation.
Also, a similar question I answered a few months ago: To what extent was the Holocaust orchestrated from Munich? And to what extent was the holocaust orchestrated by Hitler personally?