United Federation of Planets
The Federation is governed by a President and the Federation Council, both of which have offices on Earth. The means by which Federation officials attain their positions has never been clearly described. Evidence suggests that the Council consists of ambassadors appointed by the planetary governments of their homeworlds, but the appointment process for the Federation President is completely unknown. It may be noteworthy, however, that in 28 years of televised Star Trek and ten movies, there has never been any mention of an election in the Federation.
The Federation has at least one secret intelligence organization called Section 31. It is not clear whether Section 31 is entirely an external intelligence and "black-ops" agency or it also functions as an internal intelligence and secret police service.
The Federation, or at least parts of it, seem to operate on a socialist or even communist economic model. Evidence includes the lack of currency in many episodes, descriptions of the Federation's non-capitalist economy base, and government monopolies that appear to control space travel, interstellar communications, and scientific research. In any event, their society is so far removed from a free market economy that many Federation citizens have completely forgotten about capitalism. Captain Picard and Beverly Crusher are both intelligent, educated people by Federation standards, yet neither one understood the concept of investment or payment for services rendered.
The Federation consists of approximately 150 member planets spread across approximately 8,000 light-years of space, as well at least 1,000 semi-autonomous colonies. It is not clear whether this figure indicates that Federation territory is roughly spherical with a diameter of 8,000 light-years or some other shape with a total volume of approximately 8,000 cubic light-years.
In DS9 episode "Statistical Probabilities" it is predicted that Federation will suffer 900 billion casualties (both military and civilian) before being forced to surrender. This seems to suggest total population of around 1.2 to 2 trillion. If we assume population of around 6 billion for each of 150 member planets, that gives 900 billion in total. Additional 300 billion to 1.1 trillion in colonies gives average population per colony as bieng 300 million to 1.1 billion.
The Federation has technology comparable to that of the other major powers in the Alpha Quadrant. Their military readiness, however, is lacking compared to that of their neighbors. While their ships are individually powerful, often substantially more powerful than those of their neighbors, they tend to be few in number, as indicated by the perpetual shortage of ships in position to respond to military emergencies. Furthermore, many Starfleet officers do not regard Starfleet as a military organization (despite its control of nearly all military assets in the Federation), and Starfleet itself does not conduct routine combat exercises to keep its crews prepared for military action. Starship captains can often initialize "combat drills" when they feel is needed, which is logical given extreme autonomy of individual starships enjoy during peacetime operations.