In the age of hands-free pumping and adapters for your car's cigarette lighter, hand expressing is pretty much a lost art in this country. But talk to any mother who pumped before the early '90's, and you might find that her pump was her hand.
Manual expression can still come in (ahem) handy, even if you have a pump. If you get very engorged, hand expressing often works better than a pump. If you can't use your pump (on a plane with no battery pack, for example), it's great to know how to do it. If you have a really fast let down and need to express before getting your baby latched on, hand expressing is so much more convenient than the pump. And sometimes it can be nice to be able to get a little milk out before your baby latches on.
Below are two videos that show you how. The first is the Marmet technique (shown at About.com), and the second is the technique used at Stanford Hospital. You'll notice that the hand placement and motions are different. I think that both can work, and you may want to try both before settling on one.
At Stanford Hospital, the lactation consultants teach each mother how to hand express, and encourage them to do it after every feeding while in the hospital. They then teach the moms how to spoon feed the colostrum to their babies. This appears to help mothers' milk come in sooner, and I would guess that it helps reduce babies' weight loss. At a minimum, it teaches moms this really useful skill.
Have any of you had any luck hand expressing? Did anyone teach you how?