You may break into her house (in Waterfront District), open Methredel's Chest, take the diary and report back to Armand Cristophe.
If Methredel has the diary before you you can do only one thing: Steal it from her.
Open it, take the diary of Amantius Allectus and go to The Garden of Dareloth and report back to Armand Cristophe.
In the room you just entered you will find a desk.
Once you get there pick the lock and proceed into his house.
You may also give 10 coins to a beggar in order to let him mark on your map Amantius Allectus' House.
Go to Amantius Allectus House in the Temple District (follow Methredel once you fast travel).
Bring the diary of Amantius Allectus without killing him or Methredel or Amusei.
After a short introduction to The Thieves' Guild you will be told what your test is.
Then get a beggar's disposition above 70 and ask them about The Gray Fox.Choose the answer "I want to work with Hige:Join the Thieves' Guild in Oblivion Step 6.jpg|center|550px]]
Read a poster of The Gray Fox (can be found around the Imperial City), or ask for a rumor on The Gray Fox.
A Dark Elf will give you a mysterious letter she will say "take this, its from a friend".