1. Save your game, of course.
2. Determine how many picks you're willing to break before reloading.
3. Start the lockpicking mini-game. Nudge the pick.
4. If the pick breaks, immediately back out of the mini-game and start again.
5. Continue doing this until the pick moves or you reach your reload point.
The unlock point is randomly determined every time you start the mini-game. Eventually, it will be near the starting point of the pick. With each of the three locks that I've done so far, it took me between 5 and 10 picks before I got movement at the starting point. Then it took me around 10 more to actually find the sweet spot; your results may vary depending on your skill at the mini-game. Very slight movements and a good memory for the pick's position are key.