Lockpicking allows you to open locked doors, gates, containers, and safes which may contain various loot or Lead to otherwise inaccessible areas containing more loot or valuables. Like hacking, lockpicking has various difficulties. If a lock is too complex for your level to handle, your character won't even have the chance to interact with the locked object.
Most of the good stuff are hidden behind locked doors, safes and containers. Make sure to level up your Lockpicking perk to LV3 (capability to pick Expert Locks) to ensure that you'll be able to unlock most locks you encounter. You don't need to level up your perk to Master level since these locks usually have a key or locked until you progress in a quest.
Players of Fallout New Vegas and Fallout 3 can easily jump in since the mechanics are still the same. First, you need to have Bobby Pins. These are quite rare so make sure to get them whenever you see them sold at traders or offered for trade from a random settler. Bobby pins tend to break during lockpicking attempts so you can't have too many.
When you get to a lockpicking screen, the left stick controls the bobby pin's direction while the right stick controls the screwdriver's pressure direction. Position the bobby pin first then gently - and I mean VERY GENTLY turn the knob. If the controller vibrates and the bobby pin starts to wiggle, stop turning. Adjust your bobby pin's direction carefully according to how far you can turn the lock. Take note that your bobby pin's durability decreases every time it wiggles. You can preserve your bobby pin by exiting the lockpicking section after you manage to wiggle it 2-3 times. However, leaving the current screen will reset the lock's "sweet spot" and you have to "feel" it again. That said, if you're close in discovering a lock's sweet spot, a sacrificing a bobby pin or two might as be worth it.