I remember it being a rather hard technique to learn and figure out. It's hard to explain without being able to show you in person, but the trick to remember is that this technique is all about economy of motion.
The first thing you need to figure out is the proper way to have your hand rest. Your thumb sticks out straight as if you're giving a thumbs up. Your fingers, on the same hand

, should be straight and only curled at the middle knuckle of each finger. This kind of gives you a monkey paw sort of look.
Your thumb doesn't move or do any real work as the real work is being done mostly by your forearm. You bring your arm down in a motion that will have your thumb go through the string you're attacking and then land and rest on the string below it. I highly suggest just practicing this until you can get a good thump sound out of the string and your thumb always lands on the bottom string.
The next part of the motion is the upstroke. What you're wanting to do here is have your arm (again, remember the motion is in the arm and not the thumb) lift your thumb through the string. Now the way that I do this has the string slap back down on the fretboard. I'm not sure if this is proper or not, but it sounds good so I do it that way.
Now remember this technique is all about economy of motion, so when you're doing the upstroke you're also preparing yourself to do your 'pops' with your fingers. Basically, when you're doing the upstroke with your thumb your fingers should be catching the string you're wanting to pop. Just catch the string and let your arm pull your fingers through and have the tension of the string pull them down and pop them for you.
This next bit is the hardest part of the whole technique, and that's making this motion continuous and smooth. It's easy enough to get the general idea down and be able to do it once, but being able to do it nonstop is a bit of a trip. You just have to practice it. I highly suggest doing it slowly to try and figure out the sort of circular motion your arm does when you do the motion. I found that once I was able to visualize exactly what I was doing it wasn't that hard to speed it up.
Hopefully that helps you some. If not, please feel free to ask any other questions you might have. And just one more thing to note - it's not uncommon for your thumbnail to get slightly filed down by the string or for you to start developing calluses there. If that starts to happen then don't worry. It's completely normal.