The Wikipedia page is ok as a one-line introduction, but misses some detail.
Get an egg and paint a face on it.
Give it a sticky-out nose, using Blu-tack or similar.
...I'm serious...
Three lamps - LED bike lamps will probably do, but ideally dimmable lamps would help. You can use distance to control the amount of light hitting the subject - inverse square law and all that - if you can't dim them, but this will limit what you can do.
Put a bedsheet on a table, and support one end a few feet above - trap it with something - so that you have a smooth curve dropping down continuously from vertical to flat surface.
Put the egg in an egg-cup on the flat area of sheet. You'll be shooting towards the vertical wall (cyclorama) you've made.
Key light goes in front, somewhere above and to one side of the camera, above the egg 'head' height, pointing downwards to hit the 'face.' The shadow created by the nose must not hit the mouth - this is why you need a sticky-out nose on your model. Strictly, the shadow should not pass outside the area bounded by the outer edges of the eyes and the lips. The key might be a hard light from a point source. Alternatively you could use tracing paper to diffuse the light and make it softer. That's not strictly the same as a soft light (as that's more to do with the area of the source) but will suffice for experiment. However you key, you don't want to throw a shadow on the cyc.
Fill light comes from the opposite side to the key. This will normally be softer than the key. The more fill there is, the less contrast there is.
Angle? If you're the egg, looking out of the picture, the key light will normally be within 30-60
o either side of the centre line, and the fill will be more-or-less equal and opposite. The fill may be similar in height to the key, but that's not strictly necessary. Key lights can be from the 'wrong' angle too - just think how many times you see somebody in a dark room in a drama, hit using an oblique slash of light which just picks out the edge of their cheekbone. Which side to key from ? aah, that depends. Welcome to art class.
Look through the camera viewfinder - you may think all is well. You have a face lit from one side, which gives modelling to the surface. The fill from the other side stops the shaded side being too dark, without losing the modelling effect.
You're missing the back light. These are nonobvious, and require a quick history(mythology) lesson: In the grand old days of monochrome film, hair was a shade of grey, but so were the walls. How do you gain separation between subject and backdrop when they're both similar shades? Depth of field only helps some of the time (e.g. when there's a backdrop with a pattern). Thus, the invention of the backlight, which shines
forwards from above and behind the subject, and glances off the top of their head. This gives a tiny kick to the hair, which now stands out from the background. Why do we still use them now we have colour? because they work.
When you add the third lamp, your egg will truly be revealed in all its glory. If you play with the key light's angle, particularly glancing the side of the egg, you'll see what happens to skin when it's hit obliquely, and every little undulation in the surface becomes a crater. Then you can try filling the craters in with the other lamp.
Here endeth Shifty's lighting 101. If you want chapter and verse, I'd recommend Gerald Millerson's book "Lighting for Television and Film" from Focal Press, which contains more information than even
I need to know about lighting!
Of course, you
could just put your subject by a window (key) and use a big board of white polystyrene to bounce-fill the indoor side, but that would be too easy...
