I would like to propagate it but found that just cutting it off and planting did no good, so what is the correct way to do it?
This *should* work. I usually start my cuttings in a jar of water, though. Cut a piece with about 3 nodes below the growth tip. Remove all of the leaves except the ones at the tip. If the tip leaves are large, cut them in half. If you want to try cuttings in soil again, do the same process of leaf-removal, and use moist but not soggy soil. Place it somewhere with very little direct sun. Do not let it dry out.

Has anybody had any experience with this plant?
Yes! It's my #1 favorite plant. My last ones died out when I moved 3 times in 2007 - including a move from OH to AL. I was missing them so much that I special ordered from the local garden center this spring, and ended up with 10 of them.

Also, can it be kept over the winter under lights?
Absolutely. You can keep potted plants under fluorescent lights, or in a very sunny window. When you bring them inside, they will get pissed. So go ahead and remove all large leaves at that time so you don't end up picking them up off the floor later. It will probably look awful all winter but should stay alive. Do not water until it gets very dry, almost wilty. Overwatering will cause root rot since the plant is basically dormant at this time, although it might make a few flowers. You can also keep cuttings over winter in jars or bottles of water on a windowsil.

To hedge my bets, I usually bring in the potted plants, and take as many cuttings from them as possible. If all goes well, you should have several plants next spring!