Contrary to the popular misconception, even among Star Trek fans, the United Federation of Planets and Starfleet are not the same organization. Starfleet actually predates the Federation, and its history is connected to most of the time that humans have spent in space.
Although the organization and appearance of Starfleet personnel have always been military in nature, it is intended to value exploration, diplomacy, and science. These idealistic concepts lead the way to boldly go where no one has gone before.
7 Founded Sometime Between 2112 - 2136
Well before there was any talk of a united earth government or a united group of planets, it was understood that some kind of military force, not only for security but also for construction and exploration, was required for humans to continue to progress. Thus Starfleet was formed only a few decades after 2063 when Zefram Cochrane discovered warp speed and First Contact took place between the humans and Vulcans.
It was Cochrane himself, along with his friend and peer Henry Archer, who put together the early scaffolding for what would eventually become Starfleet as they developed more sophisticated warp technology. The organization would eventually evolve into a multifaceted operation over the years that included several different branches such as medical, tactical, security, and a corp of engineers along with a scientific and exploratory force.
6 Section 31 Created, The Mid 2140s
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The exact timing is unknown because this is supposed to be a big secret. The importance of Section 31 to the storyline depends on which timeline or alternate reality is featured as the setting, with these clandestine and often amoral tactics more prevalent in the Mirror Universe or the Kelvin Timeline.
Section 31 was an essential part of both Starfleet and the Federation at one point, relying on their secretive methods to gather information, and trade intelligence, and covertly disappear anyone who threatened the Federation's power and interests. Despite the Federation's open condemnation of such tactics, they were anxious to use them when it was convenient.
5 The United Federation of Planets Is Founded, in 2161
After the success of the united forces at the Battle of Cheron, which saw the human, Vulcan, Andorian, and Tellarit forces drive the Romulan Star Empire to a crushing defeat, the United Federation of Planets was founded to make the alliance official and long-standing.
The Starfleet Academy was founded the same year, and from this point on most of the main characters and heroes in the TV shows and movies were commissioned officers. The starships that explored the galaxy carried the Federation's message of peace and justice where they traveled.
4 USS Enterprise NCC-1701 Is Built, 2245
The vessel that would become the flagship of both Starfleet and the United Federation of Planets, the USS Enterprise was the greatest starship of her time. The Enterprise was named for a long line of ships, starting with galleons that were part of the British Navy as far back as the 16th century.
The launch of the Enterprise was the beginning of a new era in space travel for humanity. The era of warp 5 had begun and the Enterprise was among one of the first ships with this exciting new technology.
3 The Crisis On Tarsus IV, 2246
Not every Federation colony was a paradise. When a mysterious fungus wiped out most of the crops on Tarsus IV, the population was in danger of starvation, and Governor Kodos enacted drastic measures to ensure the survival of half the colonists - the problem was he had to kill the other half to do so. The emergency supply ships arrived earlier than expected, however, making their deaths needless, and Kodos was deemed a mass murderer.
The tragedy shook the resolve of Starfleet, the Federation, and humanity in general. It was thought that Kodos the Executioner was dead, but he appeared again decades later under a different name, Anton Karidian. The saga of how he moved for decades in disguise, and how he was finally caught, is told in the TOS episode, "The Conscience of the King."
2 The Genesis Project, 2285
In the latter half of the 22nd century, Dr. Carol Marcus made a daring scientific proposal to Starfleet Command. She and a team of fellow scientists had developed a fast and efficient way to terraform a dead planet, and needed Starfleet's help to test their theory.
The USS Reliant, with Commander Pavel Chekov and Captain Clark Terrell in charge, started looking for a suitable lifeless planet on which the Genesis probe could be tested. Their plans went awry, however, when they came across the survivors of a doomed attempt at a colony. It's Chekov that first recognizes the reference to a TOS episode, "Space Seed," in which he also starred, and things go downhill for him and Starfleet from there.
1 Praxis Is Destroyed, 2293
After the moon of Praxis was destroyed and the Klingon Empire was in danger of extinction, the military power that kept the opposing forces in the galaxy at bay was in danger of becoming obsolete. For the first time in Starfleet's history, there was a real possibility the military wing of the organization was either to be scaled back or even dismantled.
Not everyone was ready for the change. The last movie to star the Star Trek: TOS crew, The Undiscovered Country told the story of the impending end of the Klingon Empire, which began with the destruction of Praxis and continued with an assassination, a prison break, and the last voyage of the original crew of the starship Enterprise.