I've been playing around with stropping lately and have learned a few things.
Stropping is quick and effective way to finish off a decent sharpening job when you're sharpening freehand. It's difficult to maintain the perfect angle to the stone to get a polished edge just with stones when you're free-handing, but if you can get a decent edge on a knife then you can polish the edge with a strop (and proper technique) and get a good result. I'm not saying it duplicates what you can achieve with a sharpening system that rigorously maintains the blade angle during the entire sharpening process, but you can get a very nice polished edge and much improve the overall sharpness of the blade.
Making your own strop and charging it with a stropping compound.
A metal polish (I'm using Flitz) on leather (smooth or rough side--I'm using mostly smooth side) or on cardboard (like a notepad backer--not box material) makes a pretty good strop. It doesn't have a lot of cutting power, but it does a nice job of putting a polished edge on the knife.
If you're going to use a liquid polish on cardboard, get a nice, thin, even coating on it with your finger and then let it dry completely before using it. Otherwise the cardboard will have a tendency to come apart very quickly. You can easily recharge a cardboard strop with a liquid polish using the same method you initially charged it with. The cardboard will eventually start breaking down--it's disposable after all.
Flexcut Gold is a much more aggressive stropping compound that can be used on cardboard or rough side leather. In fact, when freshly applied, it actually cuts more than it polishes. You can easily see the abrasion striations it creates if you use it on an already polished edge.
Flexcut is harder to apply to the strop (they say it's like a crayon, but it's more like a really hard chalk), and if you use it on cardboard, it's even more difficult to reapply once it's stopped cutting/polishing. If you're going to use it with cardboard you need to figure that once you've applied it, then you use it until it's not cutting like you want it to and discard it. Trying to reapply it over an area of cardboard that's already been used is not worth the trouble. You might be able to clean the used area with a white plastic eraser and then reapply the Flexcut after it's clean, but I think that's more trouble than it's worth. Fortunately cardboard is usually free if you just keep your eyes open for suitable scraps.
Soft/compressible/flexible strops vs hard strops.
Leather and cloth strops tend to be soft/compressible/flexible. If you're going to use a strop in this class, you need to pay attention to how much pressure you're applying to the blade. If you push hard, you can actually defeat the purpose. What happens in this case is that the strop material sort of "rebounds" after the blade passes over it and as it rebounds, it swipes across the cutting edge and dulls it. Don't press hard when you're using a soft/compressible/flexible strop. The nice thing about compressible strops is that you can be a little sloppier with your edge angle to the strop and still get a decent result. The compressibility molds to the blade which means you don't have to get the angle exactly right.
If you're using a hard strop, like notepad backer cardboard, then as long as you are reasonably careful with your stropping angle (angle of the blade to the strop) then you can press harder. The material won't rebound and therefore you don't have to worry about it dulling the edge. Just be aware that the harder you press on a cardboard strop, the faster it will wear out. I'm not saying you SHOULD press hard, just that you can get away with a little more pressure using a hard strop.