Go to the Imperial City Waterfront district at night
Find a beggar named Armand Christophe
Raise his disposition or ask about the Thieves Guild
Wait until midnight
Talk to Armand Christophe and ask to join
Complete the introductory quest “May the Best Thief Win”
Meet the required contact and follow the quest instructions
Return to Armand Christophe after finishing the quest
You will be admitted into the Thieves Guild