The book stunner rules are complicated and don't interact well with the rest of the combat system. These rules aim to make stunners feel like a more normal part of combat while remaining uniquely useful. Note that to achieve this, some realism had to go out the window in the name of having fun, especially when you're the one being stunned.
Attack modifier, range, size, etc. of stun guns and ranged stunners are all found in Armory page 93.
Stun damage is a new type of damage based on Bashing damage.
Specific weapons are designed to incapacitate a target instead of injuring them. These weapons deal a variant of Bashing damage called Stun damage. Stun damage functions exactly like Bashing damage and can be marked as such on character's damage tracks. The exception is that when a character takes more Stun damage than their remaining health boxes, that excess damage does not convert into Lethal.
When a target rolls their Stamina to remain conscious, typically from having a full track of Bashing damage, that roll suffers a -1 penalty for every point of Stun damage they suffered before the roll.
The penalty lowers by 1 at the end of every round in which the target takes no Stun damage.
Melee stunners (aka "stun guns") require a Dexterity + Weaponry attack and deal one point of Stun damage per success. Further attacks against an unconscious target deal a static 1 point of Lethal, regardless of the number of successes rolled.
Example: Alice is assaulted by Bob and fights him off with her melee stunner. She punches him for 3 bashing, he fails a grapple, she kicks for 2 bashing, he misses a punch, and she zaps him with a melee stunner for 3 stun. Bob, with 7 health, has 7 bashing, since the extra point of Stun does not roll over. His player rolls Stamina for him to remain conscious, penalized by -3 for the 3 points of Stun damage Bob suffered.
Ranged stunners, marketed under the name Taser among others, require a Dexterity + Firearms attack to embed tiny metal prongs into the target. Hitting the target deals a single point of regular Bashing damage, regardless of how many successes were rolled. Then, the target suffers an automatic 3 points of Stun damage. On subsequent rounds, the shooter can dedicate a Movement action to keep the charge going and inflict another 3 points of Stun damage automatically. While doing so, the shooter may not use their Instant action to attack the target that they have stunned via another method, but could use it for other things, like activating a magic power, fending off some other attack, etc.
Once fired, the barbs remain attached to the firearm by thin metal wires. The target of a ranged stunner attack can use a Movement action to swipe at those wires, which automatically dislodges the barbs. Ripping the barbs out deals no additional damage (the point of bashing suffered when they hit represents all the trauma these barbs can inflict).
Since ranged stunners rely on metal probes making contact with skin, they can be negated entirely by thick clothing. Depending on what the target is wearing, aiming at other body parts (with the appropriate penalty) may allow the stunner to work anyway.
Continuing to hold the trigger after the target is unconscious deals a single, automatic point of Lethal damage instead of 3 bashing.