Section 3342 replaces the old common law rule that an owner was liable only once the dog had shown itself to be dangerous. The owner of any dog is liable for the damages suffered by any person bitten by the dog while in a public place or lawfully in a private place, including the property of the owner, "regardless of the former viciousness of the dog or the owner's knowledge of such viciousness". There is no first-bite allowance and no need to show the owner did anything careless.
The two conditions the section does impose are about the bite and the victim's presence. It must be a bite: a dog that knocks someone off a bicycle, or frightens them into the road, is outside this section and falls to ordinary negligence under § 1714. And the person must have been in a public place or lawfully in a private place. Subdivision (a) then defines lawful presence on the owner's own property generously — performing a duty imposed by state law or by the laws or postal regulations of the United States, which covers the postal carrier and the meter reader, or being there on the owner's express or implied invitation.
Subdivisions (b) to (d) carve out police and military dogs in defined circumstances: no action lies against a governmental agency where the bite occurred while the dog was defending itself from an annoying, harassing or provoking act or assisting an employee in apprehending a suspect, investigating a crime, executing a warrant or defending a person — but only where the agency has adopted a written policy on the use of such dogs, and never where the victim was not a party to, participant in, or suspected of, the acts that prompted the dog's use. Whether a victim was lawfully present, and what a bite is worth, are questions of fact worth taking to a lawyer.