Take one piece of wire and bend it into a "Z" shape using your pliers. This will be your "torque wrench," and will put tension on the lock to turn it when you move the tumblers out of place.
Take a second piece of wire and bend it so that it has a small upward point on one end. This wire will be used to push the tumblers up, so it should be small enough to fit all the way into the lock.
Place one end of the torque wrench into the lock, and apply pressure with your thumb. One end of the "Z" should be in the lock (it doesn't have to go in far), with the straight segment parallel to the face of the cabinet. The other end of the "Z" is where you can press with your thumb. Apply pressure gently so you don't bend your torque wrench.
Place the other wire, your pick, into the lock, and use it to gently probe the tumblers. Start at the back of the lock, and touch each tumbler, counting how many there are. There will probably be three or four tumblers.
While applying pressure on the wrench, find the loosest-feeling tumbler and gently push it up and out of the cam of the lock. It should click into place. If it falls back down, apply more pressure with the wrench. If none of them are loose enough to move, apply less pressure.
Repeat the process for each tumbler. Note that maintaining proper pressure on the wrench is key to your success. Too much or too little pressure may force you to start over. This can take some time, especially if this is your first time.
Once all of the tumblers are up and out of the cam, the torque wrench should suddenly give under the pressure. Use it to turn the cam as you would with a key.