Our first human endeavors venturing off of the planet started in 1961, when a space-race to get to the moon began between the US and the USSR.
It was ridiculous in retrospect, but we did it, and by 1972, when Gene Cernan stepped off the surface, and into his LEM (named Challenger), 12 people had walked -- and driven cars - Rovers -- across various parts surrounding the near side of the lunar equator. At the same time, 6 men had stayed in their Apollo Command modules and had experienced more solitude than any other human as they journeyed continuously around the back side of the moon, completely alone and cut off from Earth.
Why did we go?
You have to understand that during the 1950s, America was obsessed with communism taking over the world, just as Russia was obsessed with taking over the world with communism. So there was, what was called the "Cold War". There were proxy wars (Angola, Liberia, Iran, VietNam, Korea, Congo, Middle-East). There were assassinations (Lumumba, Diem, Castro, almost). So fierce, competition.
In this environment, both countries knew that the other had ideas for manned space flight. Neither side knew really accurately of the others' plans. Each was worried that manned flight had the possibility of unstoppable nuclear destruction. So both worked feverishly to "gain the higher ground".
Why should we have gone -- and why should we go back?
For peace, for exploration, to understand the geology of the moon and to determine, for example, if it was originally a part of the Earth that had been blown apart. We should have tried to figure if we could live there in scientific communities, with a telescope on the far side. We do this today in Antarctica. The distance from the near to the far side is a 1 hour flight. And that's why we should go back.
Anyway, it was with great pride in the USSR, (and great anxiety and frustration) in the US, when Major Yuri Gagarin made the first manned flight into LEO on April 12, 1961. Not only did Major Gagarin achieve Earth orbit. He orbited three times, before firing his retro-burners and returning safely to Earth, landing by parachute. Major Gagarin was the best of the USSR along with the technicians and engineers -- who essentially, built something from nothing. Sadly, he died in an flying accident some years later. This Wikipedia article chronicles his life.
REAR-ADMIRAL ALAN B. SHEPARD
It was the following month, on April 5, 1961, that the first american Alan Shepard, a Navy Pilot flew. He too, flew on a converted Ballistic missile launcher, a Redstone. Shepard was part of the first group of US Astronauts -- who named themselves the Mercury Seven. They made a pact that each of their spacecraft would be called the (Something) Seven, and Shepard's capsule was called the Freedom Seven. NASA's communications were -- to their credit -- pretty much open to the public. Anyway, other than sitting on the launch pad for so long, he had to use the "Urine Extractor" and was ribbed by his mates as the first wetback in Space. He finally -- with exasperation -- said "Light this Candle" and then -- largely to himself -- but to a listening world -- "God, please don't let me fuck up". His suborbital flight was a great success and the race was underway. Alan Shepard passed away on July 21, 1998. There is a lot more about Rear-Admiral Shepard's life here. His crowning achievement was working his way back to flight status, and commanding the Apollo 14 lunar landing almost 10 years later.
The "race" was on. Two or three weeks after Shepard's flight, President Kennedy -- in part trying to rescue his presidency after the abortive Cuban invasion at the "Bay of Pigs", announced that the US would undertake "to put a man on the moon before the end of the decade, and bring him home safely".
At the time of this address to congress, the US had had exactly 18 minutes experience in space flight. To say the challenge was audacious, is an understatement.
The race was underway.
The program was what we call today, design and build. While one piece of the program was being designed, the previous part was being built. This maybe ok for a building, but it proved dangerous, and deadly for the race to the moon, both for Americans and Russians.
The US program was defined in three segments:
Mercury -- to prove space flight could allow a human to operate relatively normally in a small confine and zero gravity.
Gemini -- to further advance flight systems, and to perform all the maneuvers that would be required to go to the moon, but perform them in Low Earth Orbit, and
Apollo -- to go to the moon, and to land crews there and bring them back, fulfilling President Kennedy's mission statement.
Finally, some things to keep in mind:
1. This was 1960. This was only 60 years after Wilbur and Orville's first manned flight -- the longest duration lasting less than the wingspan of a 747.
2. President Kennedy had mandated that we go to the moon in 9 years. We had had no prior orbital knowledge.
3. While the program was funded by Congress, there was significant oversight and budget cut-backs, so that the best technology solutions were often eliminated by budget constraints.