Deliver the Amulet - The Elder Scrolls IV: Oblivion
The Amulet of Kings must be delivered to a man named Jauffre at Weynon Priory. Weynon Priory is located near the city of Chorrol, which is just west of the Imperial City.
To view the World Map, first press the B/Circle button to bring up the character menu. Once on the character menu, select the Quests/Maps tab using the shoulder buttons, and then from there use the Left Thumbstick/Analog Stick to select the second tab in the row. Use the Right Thumbstick to scroll through the map.
There are two different ways to get to Weynon Priory. The most obvious way is by simply walking there; you can set “Deliver the Amulet” as your active quest. Doing so causes a quest marker to appear on the compass at the bottom of the screen.
Alternatively, you can fast travel to any of the locations that you have visited so far (though cities are available from the get-go). To fast travel to a location, on the World Map screen, move the cursor over the icon of the location you wish to travel to, and press the A/X button while hovering over it. Since Jauffre resides in Weynon Priory, that's where you should be headed next. So, to quickly travel there, call up the World Map and locate Chorrol; move the cursor down to hover over the Weynon Priory icon, and then press the A/X button and confirm that you want to travel there. It's as simple as that.
Fast travelling is a quick and easy way to cover a lot of ground in the expansive province of Cyrodiil.
Note that you cannot fast travel if there are enemies nearby. So, if you receive a message restricting you from fast travelling, scour the area for enemies, clear them out, and try again.
At Weynon Priory, you must locate Jauffre and hand over the Amulet of Kings. Upon reaching Weynon Priory, look over to the right to spot a large house. This is Weynon House, where Jauffre can most likely be found. NPCs have their own schedules and routines, and therefore don't tend to stay in one place. Jauffre should be in Weynon House during the day, along with Prior Maborel.
When you enter Weynon House, head up the stairs and turn right. Jauffre should be sitting at his desk here. If he isn't and you don't feel like looking elsewhere for him, press the Back/Select button and wait for a few hours, after which you will mostly likely return to find him sitting at the desk.
Once you have located Jauffre, speak to him and inform him that you have the Amulet of Kings. Jauffre is surprised to receive the Emperor's amulet, and goes on to discuss Mehrunes Dagon and the realm of Oblivion. Without an Emperor on the throne, Jauffre believes that the Daedra from the Oblivion realm may have a shot at invading Cyrodiil. After handing over the Amulet to Jauffre, he entrusts you with another task. It turns out that the Emperor has an illegitimate son named Martin. Your next task is to locate this man and deliver him to the safety of Weynon Priory.
Speak to Jauffre in Weynon House at Weynon Priory.
Before setting out on your quest, speak to Jauffre and select the “Assistance” option. Jauffre will unlock the chest in Weynon House, which holds some basic equipment. If you speak to Prior Maborel, he offers to give you his horse. Furthermore, if you can find Brother Piner in Weynon House, speak to him and select the “Assistance” dialogue option to receive the “Warp in the West” skill book, which increases the Block skill by one level when read. Eronor, a Dark Elf that can most likely be found walking around outside, will give you a Repair Hammer if you speak to him and ask for assistance.