2: May the Best Thief Win - The Elder Scrolls IV: Oblivion
When Armand is finished speaking, select the 'Join the Thieves Guild' dialogue option. The other two characters in the garden, Amusei and Methredhel, are both intent on joining the guild as well. Consequently, before you can become a member, you'll have to compete against the other hopefuls. The first to retrieve Amantius Allectus' diary and return to the garden with it will be inducted into the guild. This task is a simple one, provided you know where Amantius Allectus' House is.
First, you'll need lockpicks; if you don't have a sufficient amount, you can buy some from Armand Christophe at 5 gold coins per pick. Methredhel knows what she's doing, while Amusei doesn't have a clue, so ignore him. Don't bother seeking a beggar, and instead immediately fast travel to the Imperial City's Temple District. Most likely, Methredhel will be right in front of you when you appear in the district. If you haven't yet explored the Temple District, follow Methredhel to Amantius Allectus' House, otherwise use the local area map to locate his house and set a marker there.
Follow Methredhel through the Temple District to locate Amantius Allectus' House.
When Methredhel reaches Amantius' place, use a lockpick to unlock the door and enter. Once inside house, quickly approach the desk to the right. Open the desk and remove Amantius Allectus' Diary. Getting to the desk before Methredhel is easy; just run straight toward it while she takes her time. Once you have the diary in your possession, Methredhel will stop, stand up, and walk out. If you fail to get to the diary before she does, you'll need to steal it from her. It can be found inside one of the treasure chests in her home in the Waterfront.
Once you have Amantius Allectus' Diary, fast travel to the Waterfront and return to the Garden of Dareloth. Speak to Armand Christophe there and select the 'Thieves Guild Test' dialogue option to be accepted into the guild.
Getting to Amantius Allectus' Diary before Methredhel