It will be hard to explain holding them without pictures, I'll try to dig some up later (or I may just wing it with a pair of pencils)
The "lower" chopstick is cradled in your last thumb joint and rests near the tip of your curved middle finger. The lower chopstick doesn't move, or do any of the "picking", it just sits there. It also sticks out slightly farther than the upper chopstick.
The "upper" chopstick is held loosely between the thumb tip and index finger tip. This is the one that does all the work. Yes you can pick individual items off of a plate, or out of a bowl with chopsticks. The "shoveling" is done for more loose foods like rice, or noodles. Also, rice for chopstick eating (as in traditional rice) is cooked to be sticky and clump together in small balls of rice. Makes it easy to eat with chopsticks. It's us fork-using Americans that don't cook our rice "correctly" that make it hard to eat with chopsticks.
I'll try to dig up some pictures holding chopsticks off the interwebs.