Section 1714(a) is the sentence the whole of California negligence law is built on. Everyone is responsible not only for the result of their willful acts, but also for an injury occasioned to another by their want of ordinary care or skill in the management of their property or person, except so far as the injured person has, willfully or by want of ordinary care, brought the injury upon themselves. Two rules are packed into it: a general duty to take ordinary care, owed to everyone rather than only to people you have a relationship with, and the reduction of recovery for the injured person's own fault.
The words "in the management of his or her property or person" are why this section reaches so widely. It covers how you drive, how you keep your shop floor, how you maintain a stairway, what you leave on a pavement, how you supervise work on your land. The measure is ordinary care in the circumstances, not perfection and not a guarantee of safety; the section says nothing about the standard beyond "ordinary", which is what leaves the argument to be had on the facts. The final clause of subdivision (a) points onward: "The extent of liability in these cases is defined by the Title on Compensatory Relief", which is where § 3333 sets the measure of damages.
The rest of the section is a self-contained exception about alcohol. Subdivision (b) declares the Legislature's intent to abrogate a line of decisions and to restore the rule that furnishing alcoholic beverages is not the proximate cause of injuries resulting from intoxication — the consumption is. Subdivision (c) protects a social host who furnishes alcohol from liability for what follows. Subdivision (d) restores a claim against a parent, guardian or other adult who knowingly furnishes alcohol at their residence to someone they know or should know is under 21, in which case the furnishing may be found to be the proximate cause. Whether ordinary care was exercised in any particular case is a question for evidence and a matter to take to a lawyer.