On may 25,1961, Kennedy announced his support for the Apollo program as apart of a speacial address to joint session of congress:
...believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the moon and returning him safely to the earth.No single space project in this period will be more impressive to mandkind, or more important in the long-range exploration of space; and none will be so difficult or expensive to accomplish..."
At this time of Kennedy's speech, only one american had flown in space-less that a month earlier-and NASA had not yet sent a man into orbit. Some NASA employees doubted weather Kennedy's ambitious goal could be met.
A overview of the apollo project from NASA.
A explanation of what happened during the apollo 13 mission
That's one small step for(a) man, one giant leap for mandkind. Hear the audio and see the video from wikipedia.
Rockets