You can buy lickpicks from Thieves Guild members and fences, or alternatively you can in fact use the Skeleton Key, awarded from a latter quest in the Thieves Guild storyline - which we explain how to start in our Faction quests guide - which is unbreakable, but still awards experience for 'failed' attempts to pick a lock.
Lockpicking and Pickpocket are two skills which often go hand-in-hand - probably because, to gain access to locked doors, there's normally a choice available to the player: lockpick the lock, or pickpocket the key. Watch on YouTube The fastest way to max level Lockpicking and Pickpocketing