Step 1: Obtain necessary components
1) Doll head. This is a Barbie head, which may, at some point in future, be used in a rip of jessyratfink's famous Barbie Doll Electric Chair project.
2) Led. I hope I don't need to describe at length, the operation of the light emitting diode. Let's just imagine that tiny imps dance on the little chip inside, casting off photons, in their frenzy.
3) CR 2032 lithium throwie battery. Also handy if your motherboard gets old and senile.
4) Ducky tape. I could respond to those who say "It's duct tape, ya tard", by embarking on a long and convoluted aside, on the history of the stuff. whether the original duck name came from being made of cotton duck, being used to repair amphibious DUKW vehicles, it's being waterproof, and so on, but hey, Wiki it for yourself. I calls it ducky 'cause there's a picture of a duck on it.
5) Super Duper Magnet. Purty, ain't it? This one, as I'm sure everyone can tell, is from a hard drive read head electromagnetic deflection positioning apparatus. OK. voice coil.
Step 2: Attach led to battery
First, ensure that your led leads are reasonably straight. Mine are usually spindled and mutilated by removal from their previous host. Pliers may need to be used, but fingers and or teeth, usually suffice. Try to get the distance between the leads somewhat narrower than the width of your battery.
Sit the led astride the battery so that each lead of the led is engaging a battery terminal. Make sure that the lead touching the negative side isn't bent, so that it also touches the positive side. This is called a short-circuit, also known as bad.
Does the led light up? If yes, goody! If not, reverse the led. You may, at this point, test the battery with a voltmeter, or your tongue. The voltage should be about 3, the taste, slightly sour. Safety Note: expectoration is the standard safety practice, after battery tasting, lest you ingest lithium salts, electrolytes, or other nasties. Keep a spitoon, open window, or cringing assistant handy. (Get back here, Igor!)
Some may point out, at this point, that the led should have a limiting resistor, to prevent burnout (Wish I had one of those for my head). I eschew such fanciness for three reasons: 1) I don't have the led specs, to determine the proper voltage and current. 2) Since I don't pay for leds, I have little regard for their care and feeding. I rescued them from the landfill, so any life they have afterwards is bonus for them. 3) I am lazy.
Now that the led shines out bravely, keep it that way by wrapping some ducky tape around the battery / lead assembly.
The whole shebang should look like the photo. Some may complain for my not providing photos of every possible step in this construction, but, Jeez Louise! It ain't that difficult. Use your imagination.
Step 3: Attach magnet to battery
Step 4: Stick led into Barbie's head
Try to aim your led so that it illuminates Barbie's entire head, rather than just her nose. (If you have a Lindsey Lohan doll, illuminating just the nose may be more appropriate.)
Braver souls than I, may choose to enclose the entire battery inside Barbie's head as well. This should be possible, but will involve some surgery. Perhaps one could incorporate a Dr. Frankenstein's monster-like scar, or maybe a cranial screw-top, like Dr. Hfuhruhurr.
Hmmm? Maybe you could use an Al Franken doll head. Or a Ben Stein doll head. Or both stuck together... Maybe I require medication?
The assembly is secured with duct tape. (Getting kind of repetitive, huh?) One may wish to eliminate the magnet entirely, and construct a fancy high-collared robe / display stand, for the head, out of tape and one of those conical water cups. (Duxie tape and Dixie cup.) I chose not to, because such a beast would remind me, way too much, of that transparent cone-head robot, from the original Battlestar Galactica, that swished around saying, "By your command" all the time.
Step 5: Display proudly
Other applications for this device may include: earrings, freaky mobiles (the wire and string thing, you hang from the ceiling, not European cellphones) and anything else that twisted minds can conjure up.
Thus ends my Instructable, or exercise in pointless rambling, depending on one's perspective of things. Enjoy!