Instructions
Press "Start" and select the Imperial City on the world map. Fast-travel there. When you arrive, search the walls for a "Wanted" poster.
Press "X" to read the poster and learn about the Gray Fox. Find any beggar in town and talk to him. Bribe the beggar until his disposition is over 70 and then ask about the Gray Fox. The beggar tells you how to find the Thieves Guild.
Go to the Imperial City Waterfront district as midnight approaches. Head to the Garden of Dareloth, located behind the long stone wall. At midnight, Armand, a Thieves Guild representative, arrives.
Accept the quest that Armand gives you. Your task is to retrieve a diary from a man named Amantius Allectus. Press "Start" and select "Temple District" to travel there quickly.
Go towards the east wall and then take the south path. Check each door until you find the one labeled "Amantius Allectus."
Press "X" when facing the door to start picking the lock. When the lock breaks, go inside the house. Take the diary from the desk and return it to Armand to be invited into the Thieves Guild.