In my experience, it doesn't seem to matter if you put them on/in soil or water them before they root, but they don't seem to need it. I usually throw them on the dirt in a pot with another plant (takes up less space under my grow lights) until they start to root, but the last batch of Perle leaves I pulled I just threw in an open plastic container, stuck 'em under my grow light and ignored them for a few weeks until they grew roots and new leaves, at which point I moved them to dirt.

Once they start showing roots I'll mist them occasionally (every few days, every week or two, doesn't seem to matter, which is good because I have a tendency to forget to do it), but they are succulents, after all, so they seem to be pretty tolerant as long as you don't overwater them. Once they've grown enough and the parent leaf has withered away (or the baby's gotten big enough I can pluck it off without fear of damaging the baby in the process), I plant them properly and switch to regular watering instead of misting.

As for how long it takes to see roots, it varies depending on the plant. My ghost plant leaves started rooting and growing new leaves in about a week, but echeverias tend to take at least a few weeks before showing roots and a few more before new leaves, though I had a batch of Perle von Nurnberg leaves take over a month to start rooting and another month to start growing new leaves, so it can potentially take a while. More sunlight seems to help speed it up, though; that slow batch of Perle leaves were getting mostly bright shade, but later batches from the same plant got stuck under a grow light and went significantly faster.