How do you develop the knife skills to properly use a Chinese cleaver?

One important thing to keep in mind is that the blade always stays against the knuckles of your opposite hand to control it. That is true with all knives but I find it is especially important with a cleaver. (Well probably except when you are doing giant hacking moves, in which case your other hand should be nowhere in the vicinity).

I found an informative .pdf, image below. Also, youtube has videos.

Click on the image for a slightly easier to read version, but the PDF version is much clearer.

One difference in chopping is that you are doing less rocking on the tip than you would with a chef's knife. The edge stays more parallel with the cutting board. You still want to maintain the forward sliding motion while the blade moves down.

I like using a light cleaver for veggies, and find that it works better than a chef's knife with a small cutting board.

I applaud you for going over the "dark side" of knives. I find many people are afraid of using the Chinese cleaver due to it's size, weight and shape. But if you just look at most Chinese trained cooks/chefs, they basically use this one knife to do most of their cutting/slicing/dicing/mincing/smashing and food transferring. It is really something to watch a very well trained Chinese chef use one of those cleavers. In short check out Youtube.com, and just type "chinese knife skills". First hit should be "discovering Chinese cuisine part 2-Culinary knife skills". Or type in "eat drink man woman opening scene". Either one of these are going to be an eye opening and very educational clips.

I would say that the difference and how it's used is dependent on knife shape. Most Chinese cleavers are going to be a basic rectangle with very little belly (knife's business/cutting edge). But some cleavers have quite a rounded belly, these are more suited to a western trained chef. One can still utilize the rocking motion. The more straight edged cleavers are more suited to the simultaneous chop-push method.

Chop-push is raising the cleaver up and slightly back towards yourself. Then the opposite when cutting, which is down and slightly away from you. This gives you that melodic thudding sound when cutting. This method is used for most cutting, as it is a quick and efficient stroke. If you have a very sharp and heavy cleaver, you might be able to get away with just straight up and down cutting motion.

Another method is the pull back or as I call it the dragging method of cutting. This is used for cutting very tall/high/long things (large daikon radish or long pieces of meat). Have the tip of the cleaver on the cutting board and raise the cleaver's handle so that back or the middle portion of the blade is higher than what you are cutting. Then simply drag the cleaver backwards through the food until it cuts it. The weight of the cleaver is usually enough to cut the food, if it's sharp. This method also keeps the food shape with minimal deformation.

But good luck with your chinese cleaver. Have fun and don't cut yourself too much.

Practice! In addition to watching videos, reading textbooks, etc... I would just recommend to use it often. Make sure you have a nice, heavy cutting board, too.