New primary objective: Kill Vittoria Vici
Exit the Dark Brotherhood's Sanctuary and open the world map. The wedding is supposed to have place in the Temple of the Divines, but as you will get there after it ends, decide to travel to Solitude (screen above). Once you get to the destination, I suggest saving the game, so you can carefully plan your next steps and try different variants of completing the quest. You do not need to worry about the time of day, because even if you get to Solitude by night, the party would be in progress.
Markings on the map: 1 - Young couple (place of rest and a balcony located directly above it); 2 - Stairs leading to the castle walls; 3 - Interactive gargoyle; 4 - Passage leading to the balcony with Gabriella's presents; 5 - Suggested place for using the bow.
Head to the northern part of the city, to a courtyard of Castle Dour. After getting there, turn right and you should find yourself in a relatively small area adjacent to the entrance to the Temple of the Divines. The wedding party takes place exactly here (screen above).
As mentioned before, Vittoria Vici can be assassinated in few different ways, but I recommend three of them. The most obvious solution is to stab the bride. In this case it is best to approach her from behind, after she walks with her husband on the upper balcony and starts one of her speeches (screen above). After assassination you must, of course, escape quickly, because all surrounding guards will run after you (escape details are discussed later in this quest description).
The second option assumes getting on the castle walls, so you can find yourself above the area where the party takes place. I suggest going west from the Vittoria Vici place, where you'll find training guards. Once you get there, look for stairs leading up (screen above).
After you get to the castle walls, walk around the tower from the left (there is an entrance to the Thalmor headquarters). Then turn slightly right, stopping when you're exactly above the young couple. Note the unstable gargoyle there (screen above). Wait with pushing the gargoyle until Vittoria and her husband walk on the balcony located under you to begin the speech. Do not worry if you fail at first try, because she will keep returning to the balcony from time to time.
A third option is the best in my opinion. It assumes eliminating the bride with a bow. Start in the place where the wedding party takes place, looking for the small northern door (screen above).
Use the door and you'll be moved to a new balcony, from which you can see the young couple. Do not try to attack anybody yet, but look around for items left by Gabriella (screen above). These are the Firiniel's End bow, few elven arrows and a potion of true shot.
Return downstairs and head to the stairs mentioned in the description of a second variant, located on the castle courtyard west from the wedding party and leading to the castle walls (screen above).
Head now north-east, and stop when you reach the wall of the Temple of the Divines. Turn around and place yourself in the place similar to that shown on the above screen. It is important to crouch when possible and stay in hiding.
Prepare the newly obtained bow (or your own if it is better) and wait until Vittoria and her husband appear on the upper balcony to give a speech. Drink the potion of true shot, which increases damage inflicted and use zoom if possible (screen above). One arrow should be enough to murder the woman, so back up immediately after shot. This will reduce the risk of being detected.
New primary objective: Report back to Astrid
If you've chosen the fastest solution and used a melee weapon to kill Vittoria, then escaping from Solitude will be more difficult. What's interesting, you can meet Veezara on your way, which is a member of the Dark Brotherhood and offers you help in distracting some guards. Do not try to fight your opponents because you would be surrounded easily and also mages could join the fight. Instead use the sprint option, regenerating stamina if needed.
If you've chosen more subtle solution and pushed a gargoyle upon Vittoria or killed her with a bow, you'll start on the castle walls. If you're lucky, you'll stay unnoticed and even if guards are alarmed of your position, you'll be able to escape easily. Stay on the castle walls, heading south-west (screen above). This path will lead you to the tower and when you get down you'll find yourself next to the exit gate from the town. And remember that only those guards who were close to the wedding party will be alarmed about your actions. So if you see other guards next to the exit from Solitude, do not worry that they will attack you as soon as they notice you.
Leave solitude and go away to a safe distance if needed. You can now open the world map and confirm travel to the Dark Brotherhood's Sanctuary. Once you get there, look for Astrid and report her back (screen above). A main reward for completing this quest is power named Summon Spectral Assassin (you can select it in Magic section), allowing you to summon a ghostly helper. If you've killed Vittoria during her speech, you can count on bonus gold pieces. Astrid now will send you to Gabriella to talk about your next contract.
The Dark Brotherhood unlocked quest: Breaching Security