You get the quest "The Heart of Dibella" in Markarth. Locate Deagaine, usually near the Markarth main gate, or around the market.

Degaine: How about a septim? Wait, make that two septims. I feel like living it up

Ask him if he said anything about money. He says that yes, a whole heap of it. He asks if you see a temple, way up there. All them women, keeping to themselves and won't let Degaine in. But they've got a treasure in there, gold statue, size of a child. Noone knows what they use it for, but Degaine knows what he would use it for. Ask him if he wants you to steal it. He tells you not to phrase it like this because he would not want the thieves guild catching wind of us. Just go there and take it out. He will pay you half of what his man in Riften promised for it. You will be helping an old beggar.

Check under the Miscellaneous tab. You should see a new objective, "Steat the statue in the Temple of Dibella". Set the objective as the active objective, and follow the marker which will take you up the stone stairs and onto the Temple of Dibella. Enter the Temple. Senna is usually at the entrance, she informs you that the sisters are communing with Dibella and cannot be disturbed. She wants you to come back another time. But ignore her,  and unlock the Inner Sanctum door. It is an Expert Lock, so make sure you have enough lockpicks on your, or save the game if you don't so that you do not run out of lockpicks. You can also pickpocket Senna for the Inner Sanctum Key (or kill Senna), which is called the Key to the Temple of Dibella.

Enter the Inner Sanctum and head down the stairs. You will reach another door, this one unlocked. Open it, and as you enter Mother Hamal and some other sisters are praying to Dibella to guide them.

If you sneak past them, you can then go and steal the Statue of Dibella from the room in the back. Your objective now is to bring the statue to Degaine. You give him the statue, and he rewards you with some gold, which completes the objective. But, this does not yield the best rewards. Instead, let Hamal notice you. She asks what you think you are doing. You can tell her either that you were curious about the temple or that the statue looks valuable. She says you have committed a breach, and must pay the penalty. Ask her what the penalty is. She says that normally it is a quick death. But lucky for you there are more pressing matters. Instead of making an example of you, they could put you to better use. The ceremony you so rudely interrupted was the Exalted Protocol of the Dibellan Sybil. They have seen the home of the next Sybil, to the north, in a small village pressed against the stone. If you can travel there and retrieve their young Sybil, your transgression will be forgiven.

Your choices are:
I will undertake this penance. Where is the village?
I'm not your errand boy. The statue is mine.

Choose the first option. She takes the statue back if you have it. This FAILS the Misc Objective of bringing the Dibella statue to Degaine, but don't worry as you will get something better later.

 She tells you the place in their vision is Karthwasten. She wants you to move quickly - the girl must be brought to the temple as soon as possible. Your first task is to find the future Sybil of Dibella. Check your mission log, which has been updated with the details of this new quest:

The Heart of Dibella
To appease the priestess of Dibella, I have agreed to find the young girl who will be their next Sybil. It's been prophesied that she lives in the village of Karthwasten, to the north of Markarth.

Exit Markarth, and travel to the Northeast, along the river. If you had been to the Kolskeggr Mine before you can fast travel there and from there continue to Karthwasten, to cut your trip in half.

When you discover Karthwasten, speak to one of the NPCs there such as Lash gra-Dushinkh. Tell her you are looking for a young girl who lives around here. She says she thinks Enmon and Mena had a little girl, but she hasn't seen that girl for a while.

Find Enmon. He tells you their daughter, Fjotra, was taken from here. The Forsworn descended and kidnapped their little girl. When you ask him where they took her, he says it was Forsowrn from the Broken Tower. He asks what it's to you. You can tell him:
Your daughter is the Sybil of Dibella, or,
I just want her to be safe

Try the first choice. He is amazed and agrees that we need her in Markarth. He says he will come with you. Your dialog choices now are:
We'll save her together
It's dangerous out there. You should stay.

Choose the first option if you want him to come along as your follower, or the second option if you prefer to solo this quest alone. Either way, your new objective will be to Rescue Fjotra from the Forsworn.

The Broker Tower Redoubt, to the east of Karthwasten, is your destination. Follow the road and cross the bridge to reach Broken Tower Redoubt. Enter the tower, prepare to fight Forsworn forces inside such as Forsworn Pillagers and Forsworn Looters, and Foragers. Climb up the stairs and open a wooden door to the west, then head north. Locate another flight of stairs heading up. Climb the spiral stairs, and when you reach the top, exit through the door and cross into the other tower into some sort of sacrificial chamber. Defeat the Forsworn Briarheart there. Loot the Broken Tower Prison key and unlock the prison door.

Talk to Fjotra. Tell her you are there to bring her to the Temple in Markarth. She asks if it's true what they said, that she is touched by the gods. Tell her she is going to be the Sybil of Dibella. She tells you she has heard stories about the wonders of the great Temple in Markarth, but never dreamed she would ever get to see it. She is honored to being called from this duty.

Your task now is to bring Fjotra to the temple. Fast Travel back to Markarth and go back to the Temple of Dibella, enter the inner Sanctum and speak to Hamal. She will thank you for bringing the girl to her. She tells you that you have earned the Blessing of Dibella and to pray in Dibella's altar so that she can bestow her gift on you. Leave the Inner Sanctum and use the Alter of Dibella and you will get the perk Agent of Dibella which is a permanent active effect that causes you to do 10% more combat damage to the opposite sex.

This completes the quest, The Heart of Dibella.