The basic idea is to move the bobby pin to the correct position then turn the lock with the screwdriver.
The correct position isn't immediately obvious though - you have to test positions with trial and error until you find the right spot. The bobby pin shakes more when it's in an incorrect position. As you move towards the correct position it will shake less. Using the amount of shaking as a measure, you can hone in on the correct position.
Be careful though - when the bobby pin is in a high-shaking position it's easy to break it. If you don't allow the bobby pin to shake too long you should be able to try at least 2 positions without breaking it.
If by the 3rd attempt I don't think I'm getting close, I'll usually exit the lockpicking screen and then try again. This resets the try count (meaning you have more tries before breaking the pin) but also resets the unlock position. If I think I am getting close I might take a chance on a 3rd try. Sometimes it works, sometimes not.
Also, if you are playing on a console, the controller will vibrate when the pin is shaking.
EDIT: There are heaps of how-to videos on YouTube. They manage to get more than 3 tries out of their bobby pins without breaking them... but finer movements look easier on PC with mouse/keyboard controls. (I'm on PS3.)
Best Answer
It's the system in which you can pause the action a take aim at specific body parts, with known percentage of hitting them, and with each action costing a specific amount of "action points" (AP).
It stands for "Vault-Tec Assisted Targeting system", but mostly it
You can read more about it on Wikia's Fallout, Gamespy and even Wikipedia.