Skyrim:Surgery

Quick Walkthrough
# (Optional) Hear rumors about the Face Sculptor from an innkeeper or guard.
# Find Galathil in the Ragged Flagon.
# Pay her to change your appearance.

Detailed Walkthrough
Any time after installing the Dawnguard add-on, you may hear a rumor from an innkeeper or guard about someone new in Riften: ''"People say there's someone in Riften that can... change your face. Make you look completely different. Do you believe that?" Your quest journal will update with the objective to locate the face sculptor. Your map will not be updated with a quest marker, but if you travel to Riften, a guard will make a negative comment about the face sculptor, conveniently providing her location: "Take my advice, don't listen to that talk of the "face sculptor" down in the Ragged Flagon. "Face butcher" is more like it from what I've heard."'' Make your way to the Ragged Flagon, located within Riften's sewer network and accessible through the Ratway. Sitting alone on a bench is Galathil, the face sculptor you're seeking. 

Upon approaching her, she'll speak to you before you can say a word: "Hmm, I suppose I can work with your face. After all, the sculptor cannot always choose the finest clay." If you are a vampire, however, she will be able to tell and instead say, ''"What have you done to yourself? I can't work with you in this state, night-walker."'' You can ask her what she's talking about, or tell her you've already heard of her. Either way, she will subtly insult you, by implying that your appearance is not "artful" or referring to you as the "scum of Skyrim". She will then check to see if you are a client, asking "So are you here as a client? Shall I remake your face?" unless you are a vampire, in which case she'll tell you "But, my techniques only work on the living, not those that have crossed over into undeath."

At this point, you can choose to have your appearance changed, back out, or question her qualifications. If you tell her you'll have to think about it, she'll respond, ''"Indeed. It is no small thing to submit yourself to the flesh sculptor's knife."'' and begin to read a book. You are still able to approach her again with the same options if you do this. If you question her, she'll answer defensively, telling you how experienced she is: "I have not always been a ragged beggar. I learned my art from the masters of the art of flesh sculpture. I studied with the Faculty of Chirurgeons in Cloudrest. I walked with the Hollow-Faced Men of Nohotogrha for three years. I count the nobility of both the Empire and the Dominion among my clients", and then angrily add "And yet, I have fallen so low that I must justify myself to a wanderer in the sewers of this backwater of the world." 

If you decide you would like her to change your appearance, it costs 1000 gold. If you can afford it, she'll say, "Hmm. Very well. Just tell me what you desire - beauty or hideous deformity, nothing is beyond my skill", but if you don't have enough gold, she'll be offended and dismiss you: "Despite my present low estate, I am no beggar. Begone until you have the coin to warrant my skills." 

When you pay her the gold, you will enter a screen nearly identical to the initial character creation option from beginning your game. You can change almost all aspects of your appearance, the only exceptions being your character's race or sex. There is no limit to the amount of times you can repeat this quest. 

Achievements
One achievement is unlocked when you complete this quest:
 

Notes
Vampires cannot get their faces changed. You must cure your vampirism in order to start this quest.
Changing, or even overhauling, your appearance will not impair any NPC's ability to recognize you.  Therefore, it cannot be used to, for example, erase bounties or start relations over with an NPC you've fallen out of favor with by making them think you're a different person.

Bugs
 

Quest Stages