All across Skyrim you'll find loot that rightly belongs to you, but malevolent or ignorant people have separated you from your treasure by locking in in containers or behind doors. The nerve! Fortunately a bit of trial-and-error and a lockpick are all you need to restore the balance of nature and claim what should be yours.
Locks come in five grades, from easiest to most difficult; Novice, Apprentice, Adept, Expert and Master. You don't need any specific perks or skill level to attempt any grade of lock, but the higher the grade of lock and the lower your Lockpicking Skill Level, the smaller the "sweet spot" of any lock.
Lockpicking is simple; when you interact with a lock a lockpicking mini-game will begin, the goal of which is to maneuver your lockpick around a 180-degree field using the [LEFT ANALOG] stick. Apply pressure to the lockpick with your [RIGHT ANALOG] stick and, if you're in or near the right spot you'll be able to rotate the lock. If not, you'll strain the lockpick, perhaps breaking it if you damage it enough. Lockpicks, then, are the currency you pay to attempt to pick locks. If you find the "sweet spot" you'll be able to rotate the lock from its vertical starting position to a horizontal position - at which point the lock will be picked.
Note: A very good trick... well, maybe not trick but more of a tip. Try dividing the keyhole in sections. For the Master/Expert locks, try dividing the keyhole in several sections, lets say 16 parts. Start trying in each section until you see that the lock starts to turn. If it gets stuck, leave it like that and move it a tad to the right or left.
Keep in mind that picking locks is not something guards will look fondly at, not to mention the owners of said lock. It's another reason to work on your sneaking skills. Also be sure to stock up on Lockpicks whenever possible, and if you break a few picks here and there, never fear; breaking Lockpicks will make progress towards leveling up your Lockpicking Skill Score.