[paul.fr]

how exactly do they stun you? is it volts, amps or what? Also, what possible side effects (medical or other) could one suffer after being stunned?

[another_someone]

Ultimately, volts on their own are meaningless - it is (in most situations) the current that matters - the voltage merely creates the force to drive the current (and, I might imagine that in some persons, they might create temporary amnesia, which might be a blessing given the propensity to cause pain).

My understanding is that they basically overwhelm the nervous system, causing temporary paralysis (and, I believe, excruciating pain).  I believe they do not create unconsciousness, but merely muscular paralysis.

In a normal healthy human being, assuming they are used correctly, there are supposedly no long lasting effects, although with a person with a weak heart, or subject to epilepsy, or possibly other medical conditions, one can imagine quite serious side effects.  It is conceivable that if the darts land in the wrong place, and the current path is through the wrong part of the body, it might have more serious side effects.

[Bored chemist]

Last time I checked the current and voltage couldn't really be independently varied since the ratio of the 2 gives the resistance (OK, I know that might not be linear but even then you have a dynamic resistance).
The efect of an electric shock on the body is very compicated and varies with the voltage (or the current, take your pick); the duration; the contact area; the path it takes through the body; and probably the phase of the moon (OK, I'm not so sure about the last one).
I read somewhere that the record for lowest voltage leading to death was 1.5 V but, otoh,  people have also survived thunderbolts- hundreds of MV.