For a staggering blow to happen, all of the following must be true.
- You must be attacking in melee without wielding any object. (Does kicking work too? I think not.)
- You must not be wearing body armor or shield.
- You must be in your natural form (not polymorphed).
- The target monster must not be huge or gigantic and must not be thick-skinned.
- The damage dealt by the attack (with bonuses added) must be greater than 1.
- You must roll a d100 dice strictly under your bare handed or martial arts skill, where unskilled counts as 1, basic as 2, skilled as 3, expert as 4, master as 5, and grand master as 6. (This means you cannot deal a staggering blow if you are unskilled.)
Unless the monster dies from the damage, the staggering blow stuns the target monster, removes its movement points, and tries to move the monster one step in the direction away from you unless there's something stopping this.
You get a message saying something like "<monster> staggers from your powerful strike!", provided you can see the monster.
The staggering blow is most common for monks, because they are the class that can be played without body armor or shield, their martial arts knowledge lets them deal more than 1 damage with a higher chance, and they can get the highest martial arts skill.