I pretty much do the same thing as bamboo. We have it here in our office. I take care of the office plants. Typically, I end up cutting this stuff off about a 1/2" above a growth node and throwing it away, because we've filled tons of pots with it. It grows like crazy for this low light environment.
So, like Bamboo, I take a cutting, which is usually pretty long, and cut it into ~6" segments. I try to get three nodes. By node, I mead where a leaf comes off the main vine. Where the base of the leaf stem meets the main vine is where new growth comes from.
Something to keep in mind is that new growth comes from the center of the "Y", of the leaf-stem base and the vine. Typically, the vine droops and grows toward the floor, but the leaves turn up toward the light. Because of the way they're turned, it can get confusing when you're cutting it into segments. You may pull the bottom two leaves off that were turned up, only to realize they were actually the top two leaves. If you try to propagate this way, you won't have much success, because the new growth always tries to come out at the last node, closest to the end of the vine. So remember. The end that came from the pot is the bottom, and the end near the floor is the top. New growth comes from the last node, closest to the top.
Like I said, I try to get (3) nodes and I pull off the leaves of the bottom two nodes. You'll notice some scabby bumps and little black dots. These are potential roots. The bigger ones will produce roots first. They are quite large. Smaller roots will soon follow out of the small dots.
Typically, I try to do many of these at once. I usually have quite a lot of vine to work with. I'll pick an arbitrary length and cut the mother plant off here. I'll take the long vines and cut them into these (3) node segments. Typically, I cut about 1/2" above what I want to be the next top node. When you cut any plant, it will die back to the next good node, so you can save it the trouble and cut it back on the top. I do leave them long below the bottom node, because they will sprout roots.
As for potting, you have two options. One is to stick them in a jar of water. I like to use a clear jar, because it's cool to watch them root. Your other option is to stick them in potting soil. There are pros and cons to both. It's fun to watch and you get less die off in water. However, you need to pot them up soon after the roots form unless you plan to leave them in the water indefinitely, which you can if you change the water regularly or add an air stone. The reason is that once the roots grow, it's hard to pot without breaking them and they also don't like the change in environment. You get more die off when you just push the nodes into the soil, but it's a small percentage. For me, it's like 10% die off. You're doing a ton, though, and you can cut them off and keep propagating the pot as they grow too long. You need to keep the soil pretty wet till you see new growth, though. Then you can let it dry out a little. They prefer to be wet, but can dry out without a lot of damage. If you let them go too long, you'll loose a vine, but typically you loose just one if you start watering again. I've never had them all die off.