Breakdown of the Federation Government
The Federation Government is currently composed of 3 main branches of power. The Executive Branch, composed of the office of the President and their cabinet, the Legislative Branch which includes the Upper House, the Federation Council, and the Lower house, the Federation Legislative Assembly and finally the Judicial Branch.
The governmental system the Federation uses is modeled on/influenced by the Democratic Federal Parliamentary Republic. (For more information and a real-world example go here.)
This branch is self-explanatory. The President and his party are voted in by the public, after which the President creates his Cabinet. There are two ways to be put in the Cabinet, appointed or voted in. People holding the post of Minister in the Cabinet are either appointed by the President or come from within the voted electorate and serve a dual role as the minister and represent their riding within the House.
In the Legislative branch, you have the Upper House and the Lower House.
For the Upper House, the Federation Council, members are appointed to this council by the governments of member worlds. So, Earth appoints their Councilor, Vulcan theirs. Those that hold these positions are generally in such a position until such a time as their own government decides that they may no longer needed. As such, some Councilors such as the great Sarek can hold the position for decades as long as the government is satisfied with their service, while others could hold the position for months before being removed.
The Lower House is the one that the general public votes in to represent them. Each planet has a certain number of seats, generally set by population size, that are contested in each election. The party that holds the most seats in the Lower House makes up the government.
Currently, the ruling party of the Federation in Obsidian Fleet is the Planetary Protection Party – “Federation now, Federation Forever.
The Planetary Protection Party is a mid-right party on the political spectrum. They hold government via a coalition majority with the Alliance for Planetary Freedom – “Securing Today against Tomorrow’s Threats”.
The Opposition party is currently the Federation Unity Party – “We March Towards the Stars.” The Unity party is a Centralist party on the political spectrum, and for decades before the Mars attack as the ruling party.
The fourth party, the United Colonial Front – “United in Struggle, Together in Victory” is on the left side of the Political Spectrum, a more social democratic party.
Honestly, not much to write on this one.
There are three tiers to the Judicial Branch, the Supreme Court of the UFP, the Circuit Courts of the UFP then the Planetary Courts of the UFP. The basic Judicial structure is the same as most modern-day countries in which cases should start at the local level before making their way up the ladder until they reach the Supreme Court.