First, I highly suggest reading the novel Articles of the Federation, as it provides deep insight into the inner workings of the Federation government. Only pieces of the workings of the UFP government have ever been revealed on-screen. What is most likely is: It appears to have a check-and-balance system of Executive, Legislative, and Judicial arms.The Legislature is a unicameral government (consisting of only one assembly).Unlike having two separate legislative assemblies like the U.S. Senate and House, or the U.K. House of Lords and House of Commons, the Federation Legislature consists of only one body, simply The Council.The Council is responsible for far-reaching decisions affecting the entire Federation, such as ratifying new amendments to the Constitution, declaring war or peace, and approving new member worlds. They also hold a lot of influence over Starfleet, with the military organization required to seek approval from the Council for major engagements, such as the Romulan-Klingon border blockade during the Klingon Civil War. It is not clear exactly how much autonomy Starfleet and individual Admirals and Captains have regarding planning. Presumably they can plan their own engagements on the local level. It could also be possible that the Council gave Starfleet more autonomy during the Dominion War to increase action time (i.e. no waiting for the Council to make a decision for every Operation).The Council oversees foreign policy (i.e. anything having to do with diplomacy and interaction with outside powers).There is some debate as to where the Council meets. In Star Trek IV, it appears that the Council Chambers are located in San Francisco, where Starfleet headquarters is located. However subsequent on-screen appearances explicitly mention that the Federation President's office is located in Paris, and subsequent novels have assumed Paris, and the Palais de la Concorde is the seat of government.Some have speculated that there is more than one location for assembly. The primary chamber could be located in Paris, but a secondary one in San Francisco.Like governments today, various representatives also sit on "Sub-councils" or "Committees." Examples include the Security Council, which oversees the security of the Federation, and the Judicial Council deals with law, possibly overruling the Supreme Court if enough votes are accumulated.Non-canon references (those not seen on-screen, but mentioned in novels and such) explain that it is left to the individual member worlds to choose their Council members. It is unclear how many representatives are allotted for each State. Watching Star Trek IV, it looks like at least two representatives.For example, on Bajor, the First Minister nominates an individual, which must then be approved by the Chamber of Ministers.Andoria's is decided based on which political party holds the majority in the Parliament Andoria.Betazed holds a popular election.Being chosen as a Councilor was considered a great honor, and as of 2266, only T'Pau of Vulcan had refused a seat.The Executive Branch consists of the Federation President and their Cabinet. They are responsible for the day-to-day decisions of the Federation. They are widely considered the most powerful person in the Alpha and Beta quadrants.They serve as commander-in-chief of Starfleet, and issue most orders, though as said above, major decisions may have to be approved by the Council.The President appears to be elected by popular vote, but it is not clear how this is accomplished. There are billions upon billions of citizens in the Federation. In the era of supercomputers, it is entirely possible that billions of votes can be individually tabulated. Another option that I think might be possible is that each planet holds a popular vote, and the winner of that planet is awarded one point. Ultimately, the President is decided by a majority of points, around 150 at the time of First Contact (for 150-ish planets). Think of the U.S. Electoral College, but not as biased.Another theory is that they are elected purely through the Council, but that kind of defies the point of a popular democracy. Then again, it drastically simplifies the vote-counting from billions to a couple hundred.The initial candidates seem to be nominated by their member worlds, which are then approved by the Federation Council (perhaps to prevent a single world from nominating too many at once?).They serve four-year terms, but no on-screen information is available concerning re-election. Some novels show that it is possible, such as Jaresh-Inyo (from DS9s "Homefront") being defeated in re-election. (Honestly, after that turmoil by the changelings and Dominion, I wouldn't run again!)The Cabinet is the collection of individuals within the Federation government who serve as the heads of the various executive departments of the Federation government and as the principle advisers to the President of the United Federation of Planets.The President appoints cabinet members, who are then confirmed by the Federation Council.The cabinet is also said to include some members who are not the heads of executive agencies, but whose access and seniority is equal to that of the heads of executive departments.Supposedly, Section 31 had an agent inside Jaresh-Inyo's Cabinet.Form of Address:"Mister President" if a male (any species) (TOS movie: The Undiscovered Country)"Madam President" if a female (any species) (ST novel: Articles of the Federation)"Zha President" if a zhen (Andorian) (DS9 novel: Andor: Paradigm, ST - The Fall novel: Peaceable Kingdoms)"Sha President" if a shen (Andorian) (DS9 novel: Andor: Paradigm)"Cha President" if a chan (Andorian) (DS9 novel: Andor: Paradigm)"Tha President" if a thaan (Andorian) (DS9 novel: Andor: Paradigm)"Shir President" if an asexual president (of any asexual species)The Judicial Branch is the least-known.The only on-screen mention seems to be the Federation Supreme Court.The only thing we know for sure is that it is the highest law in the land and has final say (but if there exists a checks-and-balances, the President or Council can probably overrule a ruling).There are at least two fundamental documents underlying the Federation: the Charter of the United Federation of Planets, and the Constitution of the United Federation of Planets. It is never made clear on-screen which document oversees what, but some writer theories propose:The Charter details the requirements of a planet to be considered for admission to the Federation. Known requirements include:Caste-based discrimination is forbidden. (Does this mean some discrimination is acceptable?)Officially, the UFP is forbidden from interfering with the inner workings of a sovereign state.Unofficially, Section 31 "interferes" all the time.Excerpt, as seen in VOY - "The Void": The Constitution details the rights of citizens and responsibilities and limitations of the UFP government.At the most fundamental level, the Constitution consists of twelve "Guarantees" (amendments)The Seventh Guarantee against self-incrimination during legal proceedings was considered by Captain Picard in 2367 to be "one of the most important rights granted by the Federation." (TNG: "The Drumhead")The Twelfth Guarantee of the Constitution dealt with the rights of artists, and defined an artist as "a person who creates an original artistic work". (VOY: "Author, Author")In some instances those protections related to fundamental rights can be extended to non-citizens while on Federation territory (such as a Starfleet vessel). (TNG: "The Perfect Mate") Note that there is also the Starfleet Charter which dictates the rights, responsibilities, and limitations of Starfleet - the military, scientific, and exploratory arm of the Federation. This exists separate from the Charter and Constitution. ---- One question I have that is never alluded to are Political Parties. Presumably, with so many lifeforms and individuals, innumerable differing opinions exist on how to run the government. Are there Conservatives and Liberals (or the equivalent thereof)? Presumably, there also exists fringe parties as well. I wouldn't be surprised if the pro-Human, pre-Federation Terra Firma exists in some form in the 24th century. ---- I could go on, but my fingers ache now.