While exploring through the Elder Scrolls Online you’ll come across locked treasure chests. In order to pick the lock you need lockpicks, that can be obtained from chests, drawers, boxes, wardrobes scattered all over the world, or you can buy them from vendors.

How to pick a lock in TESO
1)Position the lockpick over a pin. You can position over any pin you want, there is no particular order in which you have to pick the pins.
2)Press and hold down your left mouse button until the pin starts wiggling
3)Release the left mouse button as soon as it starts wiggling or you will break your lockpick. If you release too early or too late the pin will reset, and you have to start over with the same pin. For harder chests, you have less time to do that, thus, try not to repeat any of the pins, try to do them doing the first time.
4)If you’re successful, the pin stays locked down when you release the mouse button
5)Move the lockpick over the next pin and repeat

Don’t forget that you have limited time for this activity, until the timer bar empties, or the lock piking will fail, and you’ll have to start over. Some locks are more difficult to pick than others, so practice with easier ones. Practice makes perfect, so in time you’ll learn to release the mouse button even before wiggling starts.