The United Federation of Planets' federal government has three branches. They are: an executive, led by the Federation President; a legislature, the Federation Council; and a judiciary, whose highest court is the Federation Supreme Court. It is unclear whether the executive and legislative branches are "fused", as in the Westminster system, wherein the President and the Cabinet are also legislators, or whether the executive is separate from the legislative, as in the American Congressional system.
The four founding worlds are Vulcan, Andor, Tellar, and Earth. The Federation's collective aspirations are comprised in a founding Charter, called the Federation Charter, which is analogous to the United Nations Charter. The Federation is governed and and its structure defined in a Constitution, the Federation Constitution, which is comprised in part of a bill of rights consisting of Guarantees, such as the Seventh Guarantee, which is similar to (and probably inspired by) Amendment V to the United States Constitution.
As of the time of Star Trek: First Contact, the Federation has one hundred fifty member planetary governments across eight thousand light years. The member planetary governments, as the name "Federation" suggests, have delegated some of their former sovereignty to the Federation federal government, and retained the remainder. The Federation agency that is most familiar is Starfleet, an exploratory armada of starships, starbases and planetary outposts.
Prospective members must, as a threshold matter, have independently developed warp drive. Also, non-member worlds, selected for "first contact" by the Federation, must have warp drive capability, or else the Prime Directive of non-interference (which is also codified in Starfleet Regulations as General Order Number One) applies, and, as a result, the Federation and its Starfleet are prohibited from revealing their existence to such worlds, absent extenuating or exigent circumstances. The Federation expands as a result of facilitative diplomacy, and has a diplomatic corps to that end.
The Federation's most significant enemy is, by far, the Borg. Also, the Federation has been, on occasion, confronted by belligerents such as the Romulan Star Empire, the Cardassian Union, and the Dominion. Currently, the Klingon Empire is entered into a formal Alliance with the Federation, but up until approximately a century in the past it was also a belligerent. One significant non-member associate and de facto ally is the Bajora, which, under occupation by the Cardassian Union, had a government-in-exile called the Bajoran Resistance, but Bajor has since been liberated and is under a provisional government ProfessorTrek 16:44, August 12, 2011 (UTC)