Short answers, pulled from the story.
The Three Laws of Robotics are: a robot may not injure a human being or allow one to come to harm through inaction; a robot must obey human orders unless they conflict with the First Law; and a robot must protect its own existence unless that conflicts with the First or Second Law. They first appeared together in the 1942 short story "Runaround".
All three laws appeared together for the first time in "Runaround", published in 1942. The story was later collected in the 1950 anthology I, Robot. The First Law had appeared alone in an earlier story, "Liar!", and similar ideas were implied in even earlier work.
The origin is contested. Asimov attributed the Laws to a conversation with editor John W. Campbell on the 23rd of December 1940. Campbell believed Asimov had already formed them. Asimov's friend Randall Garrett proposed they were a symbiotic creation of both men, a version Asimov accepted.
The Zeroth Law states that a robot may not harm humanity, or through inaction allow humanity to come to harm. Asimov added it to precede the original three, with lower numbers taking precedence. The robot R. Daneel Olivaw was the first character to name it, in the novel Robots and Empire.
The character Elijah Baley identified in The Naked Sun that a robot could unknowingly become a murder weapon if it was not aware of the harmful nature of its actions. A criminal could also divide a lethal task among multiple robots so no single robot recognized its role. Asimov's own later novels suggest that robots obeying the Laws perfectly could harm humanity by suppressing human initiative and risk-taking.
In March 2007, South Korea announced it would issue a Robot Ethics Charter that might reflect the Three Laws. In 2010 the UK's EPSRC/AHRC working group published a set of five robot principles, the first three of which updated Asimov's Laws. Science fiction author Robert J. Sawyer argued in 2007 that military and commercial interests made such laws unlikely to be adopted by industry.