So what did Sartre say? Basically, he simply denied that we have any natural traits (i.e., essences, characteristics). Instead of such essences, Sartre said, we have existence, and that's it. Our essences don't really exist. At best, they have a secondary reality because we first exist, then select our essences. In his words: “[M]an first of all exists, encounters himself, surges up in the world–and defines himself afterwards.”
As a corollary, Sartre said there are no immutable rules of behavior that a man ought to follow because rules of behavior stem from our natural traits. Even intellectuals who reject God or disregard Him in their theories always posit some immutable characteristics and pull rules of behavior from them–for example, “man is a social animal, and therefore he should act civilly toward others, not kill, not seduce other men's wives, nor otherwise hurt others.” Sartre, on the other hand, rejected any immutable characteristics, and therefore rejected the idea that there are any truths that emanate from those characteristics. There is only one truth, he said: The stark naked fact of existence.
A logical reaction to this type of reasoning is despair. If there is no truth, there is no reason to act whatsoever. All actions–and potential actions, plans, aspirations, and dreams–become pointless, along with one's entire life (reference the stranger, Mersault). But Sartre didn't stop with despair. He used his existentialism to teach a new form of radical freedom: If there is no way you should act, he said, then act however you want. Make your own essences.