Join the Thieves Guild
Complete the Thieves Guild questline up to the quest “Nocturnal”
Travel to the Shrine of Nocturnal
Speak to the statue of Nocturnal
Receive the Skeleton Key as the quest reward
Keep the Skeleton Key until you return it during the quest “Nocturnal” if you want to finish the questline
If you want to keep it permanently, do not complete the quest and do not return it