I pretty much stumbled into this quest, but to get it to trigger you need to head to the Temple of Dibella in Markarth . In it, the priestess will tell you that the temple is closed. Bah, who listens to authority figures!? Head to the inner sanctum door and pick it ( alternately, you can pickpocket the key from the priestess ).
Once inside the inner sanctum, if you're sneaky you can go around and steal all sorts of goodies. You will hear the three priestesses in here asking for a sybil. Now, intentionally get caught by them. Yep, trust me.
You will end up talking to their leader, Hamal. Tell her you were curious about the temple (don't just murder them all!) and after some threats and some chatting, she will make you start this quest as "penance" for your intrusion.
Note: I've had the other priestesses attack me here even when I tried to stay friendly. If that happens, try re-loading your auto-save and it shouldn't be a problem.
Well now, it looks like we're off to the town of Karthwasten to try and find the new Sybil. Head north to Karthwasten and once you are there talk to just about anyone about the young girl you are looking for. They will all tell you to go talk to Enmon, making him your target.
Go talk to him (he's a miner) and he will be pissed off, assuming you are taunting him as the Forsworn have taken his daughter. Tell him that his daughter is the Sybil of Dibella and he will agree that we must rescue her and will join you (you can choose to leave him behind, but I let him come). The forsworn are holding her at Broken Tower Redoubt, to the east.
Head down the road to the north and past a bridge and you'll be led right past the tower. There will be some forsworn outside and some archers up above, so just kill what you can and head inside. You'll encounter around three forsworn in this first wide-open room, so take them out (you can use sneak attacks). To the left of the stairs is a pantry you can raid that has potions at times. Go up the stairs and right, following the hallway but BE CAREFUL of the two traps that are set up.
Past the traps is a sleeping area. You can kill another forsworn here, but the real treat in this area is a BLOCKING SKILLBOOK called "The Mirror" on a nearby bookshelf. There are a few chests scattered about too, so loot away. Continue through a side door (the one that doesn't lead back out to Skyrim) and follow the linear path to a staircase.
You'll fight 2-3 forsworn on this staircase. Don't rush them, or if you do you may run into a falling boulder trap that they've set-up on the stairs (honestly, THEY set it off themselves more often than not). Some of these forsworn may be mages too, so break out the big guns (or goad them into melee attacking). Follow the stairs up as high as they'll go to reach the door back to Skyrim that the objective marker is telling you to go through.
Get ready for a fight! Head through the door in front of you and you will end up facing a forsworn briarheart well-versed in ice magic! Keep your health up and beware of his icewave attack and you'll be ok (drink some ice resistant potions if you must).
Once he is dead, loot him for goodies and the prison key. Also, there is a CONJURATION SKILLBOOK named "Liminal Bridges" on one of the tables in here. There is a shrine of Dibella nearby and a BIG treasure chest in a bedroom here as well. Once you're done looting, open the prison cell and talk to Fjotra.
Tell Fjotra she is the new Sybil and she'll accept it gladly and wants you to take her to the temple right away. Now, if you killed everyone you can just fast-travel to Markarth (I ran through the place again since I missed one enemy and Fjotra would say "Eww, a dead body!" whenever she saw a corpse). And even though I took her dad, he didn't survive, so when she saw her dead dad she said "Oh no, this can't be happening", but didn't seem too distraught over losing her father...
Take her to Hamal and she will be amazed you found her and brought her back. The quest isn't quite over though, you need to head back to the main part of the temple and interact with the basin in the middle of the room to receive the blessing:
o AGENT OF DIBELLA: You do more combat damage to the opposite sex.
And with that, the quest is over.
Note: Hamal will now train you in ENCHANTING if you wish. She is the MASTER trainer in enchanting.