To join the Thieves Guild in The Elder Scrolls IV: Oblivion, follow these steps:

1. Discover the Thieves Guild's existence
   There are several ways to find out about the Thieves Guild:

   • Commit a crime (like stealing) and get caught. Serve your jail time, then after release, someone will approach you with a note inviting you to meet the guild.
   • Investigate wanted posters of the Gray Fox found around the Imperial City. Ask guards about the Gray Fox until you learn that "the beggars love him, especially in the Waterfront."
   • Raise the disposition of a beggar named Puny Ancus in the Waterfront District by bribing him until he reveals information about the Gray Fox and the guild.
     Alternatively, you can just go directly to the Garden of Dareloth in the Waterfront District without prior knowledge and still trigger the initiation event

2. Go to the Garden of Dareloth at midnight
   The Garden of Dareloth is located behind the Abandoned Shack in the Waterfront District of the Imperial City. Arrive there at midnight to meet Armand Christophe and other aspiring guild members. This will start the initiation quest called "May the Best Thief Win"

3. Complete the initiation trial
   Armand will challenge you to steal a diary from Amantius Allectus' house in the Temple District. You must be quick because you are racing against two other thieves. The house is located by following the eastern path in the Temple District, then turning right into a small alley. The diary is inside a desk on the right wall of the room.
   Lockpicking is required but the lock is easy to pick. Alternatively, you can follow an NPC named Methredhel who will lead you to the target.
   After stealing the diary, return to Armand at the Garden of Dareloth to complete the quest and officially join the Thieves Guild

4. Benefits after joining
   Once a member, you gain access to fences who buy stolen goods, and you can start the Thieves Guild questline, which involves various theft-related missions. You also get access to special gear and perks suited for stealthy gameplay

In summary, you either get caught stealing and wait for the invitation, or investigate the Gray Fox's wanted posters and beggars in the Waterfront, then meet Armand at midnight in the Garden of Dareloth to start your initiation trial by stealing a diary from Amantius Allectus' house

. Completing this trial officially inducts you into the Thieves Guild.