When you reach Kvatch, you'll be told that the whole city is destroyed by forces of evil. Go up the path and meet Savlian Matius, local guard captain. He will ask you to close the Oblivion gate nearby. Agree to that, defeat some enemies, and cross the gate.
Well, here you are. Oblivion. Go to the left and follow the path to the end. Watch our for enemies and some rocks falling from the cliff. To the right, you'll see some mean looking towers. Go towards them and enter the biggest one.
When you're inside The Blood Feast, get rid of some enemies. Your goal now is to reach the top of this tower. Go through the door to Rending Halls. There go to the central room (the one with fountain in it) and use the door to get back to The Blood Feast. Go up and enter Corridors of Dark Salvation. Find the exit (to Plane of Oblivion) and cross the bridge to Reapers Sprawl. You'll hear a voice calling for help. Go to the top of the tower and you'll face a mini-boss - Dremora Sigil Keeper. You'll find a key when you search his body. Talk to the prisoner and go back to Corridors of Dark Salvation. Use the key and go up, finding yet another door to The Blood Feast. Enter the moving platform. Continue going upwards until you reach Sigillum Sanguis. Enter the central room in there and reach the top. Touch the Sigil Stone, and you'll find yourself back in Kvatch. Kudos, your first Oblivion gate is down. Go talk to Matius and tell him you're ready to enter the city.
A short battle on the market square follows, nothing big after walking through hell itself. Once you deal with all the monsters talk to Savlian and enter the Chapel. There you will meet Martin, the Emperor's son you are looking for. Tell him about everything and he'll gladly join you back to Weynon Priory.
There, it turns out the place is being attacked by the very same cultists that took care of the Emperor. You'll find Jauffre in the Chapel (a small building to the right). Talk to him and go to his office, when you'll find out that the amulet is gone. Talk to everyone. You will agree to go to Cloud Ruler Temple.