Hobbes begins from an observation about natural equality. Human beings are roughly equal in strength and intelligence: even the weakest can kill the strongest by cunning or coalition. This equality is not a foundation for cooperation — it is a source of conflict. Because no one is so powerful as to be permanently secure, everyone has reason to fear everyone else. From equality comes competition; from competition comes distrust; from distrust comes war.
The state of nature is not a historical era before civilisation — it is a logical condition that obtains whenever there is no effective common power. Hobbes finds evidence for it wherever central authority has collapsed: in civil war, in the relations between sovereign states, in the life of frontier settlements. It is the condition that politics exists to prevent.
The consequences of the state of nature are total. Without security, no long-term project is possible. Without long-term projects, no economic life is possible. Without economic life, no culture, no science, no art. The list of absences Hobbes compiles is deliberately overwhelming: he wants the reader to feel the weight of what political order preserves, precisely because we are so accustomed to it that we take it for granted.
In the state of nature, every person has a right to every thing — including the body of every other person. This follows from Hobbes's account of natural right: each person has an unlimited right to whatever they judge necessary for their own preservation. Since there is no law and no authority to say otherwise, this right has no limits. But a right to everything that no one can securely exercise is effectively a right to nothing. The state of nature collapses into a condition where rights exist in theory but cannot be enjoyed in practice.
This is not a description of human nature as essentially evil — Hobbes is careful to distinguish his view from misanthropy. People in the state of nature are not malicious; they are rational. Their violence is pre-emptive, defensive, and entirely understandable given the situation. The problem is structural, not moral. And a structural problem requires a structural solution: not the reform of individual character, but the creation of a common power capable of making cooperation rational.
The state of nature argument appears in Chapters XIII and XIV of Part I. Hobbes's famous list — "no place for Industry... no Society" — and the phrase "solitary, poore, nasty, brutish, and short" appear in Chapter XIII.