There are various statements of the non-aggression principle (abbreviated NAP, or ZAP, Zero-Aggression Principle) (Wikipedia). I like Rothbard's statement of it:
No one may threaten or commit violence ('aggress') against another man's person or property. Violence may be employed only against the man who commits such violence; that is, only defensively against the aggressive violence of another. In short, no violence may be employed against a nonaggressor. Here is the fundamental rule from which can be deduced the entire corpus of libertarian theory.This statement is good for specifically calling out self-defense. Note that aggression is against person or property (since a person owns themselves, there's some redundancy there). Frequently phrases like "the initiation of force is wrong" (or "aggression" for force) are used; initiation makes it clear that self-defense is not considered wrong; self-defense also includes hiring agents to defend you (although they have no special rights).
— Murray N. Rothbard, A Libertarian Theory of War
It is not specifically spelled out in the NAP, but libertarian thought usually allows only for commensurate defensive response (killing someone for stealing a loaf of bread, except in extreme circumstances, would likely be considered initiation and not response). The idea is to use necessary force to stop a threat—not pull punches, but neither cruelty or continued force when the threat is neutralized are part of self-defense.
Also external to the NAP is the idea of justice after the fact. Rothbard's "infringe as you were infringed", Block's "two teeth for a tooth", and Kinsella's "applied estoppel" principle are all good sources here. Please see the sources for Recompense for Fear: Is Forced Russian Roulette Just?.
Note too that the NAP is a principle, not a group of armed thugs. You won't meet it walking down the street. It is not self-enforcing; it cannot be. It can be violated, just like, say, the principle of "pacifism" or the Golden Rule, and it may be that nothing bad will happen to the violators. It's a just and moral principle for association in a free society; nothing more, nothing less.
It also is probably not enough for most people. It is a minimum; most religions would not call a person "good" (or virtuous) if they merely refrained from harming people. Beyond it, help to the truly needy (the Bible mentions widows and orphans in particular) is a command of many religions and something many people, religious or not, would require of themselves. The NAP just says it is wrong to coerce it.
Also see:
The Non-aggression Principle - various interpretations.
The Non-Aggression Axiom of Libertarianism by Walter Block