First the quote for reference (from YS156):
Riposte: On a successful defense with Weapons, you may sacrifice your next action to turn that defense into an immediate and
automatically successful attack. Your attacker must be within range
of your weapon, and if you’re mounting a full defense (page 199) you
do not get the benefit of the +2 bonus when your defense roll converts
to an attack roll.
My interpretation of this in my campaign has been that your successful attack is how many shifts you received on the defense roll, i.e. you treat the riposte attack with the shifts of success that you made on the defense roll as your success on the attack roll, and add the weapons rating to that attack roll to determine damage.
Kassandra at Weapons +4 is engaged by a Cultist who has Weapons +2. She's armed with a knife (W:1) against the Cultist's ceremonial blade (W:2). Since he has reach, she decides to delay her attack to see what he is going to do.
He rolls +2 on attack, for a total of +4. She rolls +1 for a total of +5, and decides to riposte. Her defense was 1 shift higher than her opponent's attack, so her attack is automatically a 1 shift attack, and does +2 damage to her opponent.
Now, the part that I'm not sure of is when you can add aspects, i.e. would Kassandra have had to add aspects on her defense roll- or can she add a more aggressive appropriate aspect on her attack, since she's not rolling.
I've ruled the latter in my game, as she's having to give up her action in order to power the riposte.
TL;DR - you use the difference in shifts on the defense roll as the attack result, add any applicable weapon rating, and can add aspects, though you don't roll.