Alas, there are no manuals or books on "how to do skeleton." You'll need to consult with a qualified instructor, of course, but I've come up with a list of basic tips:
1) First, see if you're even allowed to slide. You may be ineligible if you: have a serious neck injury, are too large for the sled (e.g. morbidly obese or extraordinarily tall), lack health insurance, etc.
2) Beforehand, familiarize yourself with a map (or helmetcam video if available) of the track so you can anticipate the curves rather than feeling lost.
3) Have proper safety gear. Often provided for you are: helmet with visor, and track spikes (same as those for track & field)--which allow you to walk on ice. And you'll often need to bring your own gloves, mouthguard and elbow pads.
4) You're not allowed to carry anything (e.g. phone, camera, pocket change, or wearing a watch) that could fall onto the track or be damaged by impact.
5) Try not to use a helmet that's too big (or too small, which may yield a slightly busted chin or nose) and make sure it's fully strapped in before you start. My one near-death experience in this sport (which was actually recorded on a blurry video) was when my helmet mostly popped off during a slide.
6) During the ride, it's important to always keep your hands on the sled handles.
7) Try to maintain an aerodynamic shape--arms tucked in tightly, keep legs straight and together, not craning your neck high up in the air.
8) Relax. Although you may initially be terrified, by the time you're finished you may be eager to do another run.
9) Regarding injuries, I think you should be OK if you're just taking a 1-day class. In my sliding classes (your experience may vary), most folks emerged unscathed or with just minor arm bruising after the first few slides (short rides from the junior starting gate). Although for those who returned in the following days to take additional slides from the top, the bruising/injuries became substantial for a few sliders (unbearably so, for a couple of folks), but nothing serious. I've noticed that the wider your body is, the more susceptible your arms are to getting banged up.
10) You'll also learn about body positioning and finding your balance point on the sled, steering with your head and shoulders (or using your knees or dropping a toe), and track physics (such as steering through double-oscillation curves). I also posted a few random tips in this old newsgroup posting. A qualified instructor will show you all this stuff in person, good luck!