I have half a dozen adult succulents and have been conducting some casual research on how to propagate them. (Propagating succulents sounds like a good band name.) You can pretty easily make a baby succulent just by using the leaf of an adult succulent. I've tried several different methods that I've found online, but what is depicted below was the fastest/ easiest.
I believe this is a Graptopetalum (a "ghost plant"). Go through your succulents once a week and gently wiggle some of the lower leaves. If a leaf has some give, you can remove it without ripping the plant. Some practically fall off on their own. If you have to struggle, leave that particular leaf alone.
Lay the leaves out (several different species are here) for a day or two to dry them out. If you skip this step, the leaves will rot rather than budding.
Closeup of leaves. Note that the break point is pretty clean.
I tried several different methods, and the water-based method was best. At first I tried a more standard method where you take the leaves after having dried for a couple days and lay them down on a thin bed of soil. Spritz the soil every day with water. This does work--about half the leaves will bud, and half will rot. However, this method works faster, and results in fewer rotted leaves. Take a cup, fill it up halfway with water, tightly secure it with some plastic wrap, then use a knife or paperclip to make some small holes in the top. Take the leaf and either put the open end of it very close to a hole, or gently push it slightly inside the hole. Leave the cup in a sunny place, and it will basically take care of itself.
The first thing that will happen is that a small bud will emerge that looks like a tiny flower. The bud will continue to emerge along with these thin, spidery roots (seen above) that start to reach down into the water.
Once they've developed a good amount of roots you can plant the buds into a planter with other ones. Some won't really make it, but at this point they're pretty robust. I spritz mine every morning with water. If you travel, don't worry about it too much-- they don't actually need a lot of attention and can go a few days without water.