Because this is an educational project it's intended to be inexpensive at scale. There are only two electrical components (the LED and the battery) and if you buy them in bulk, and use the full roll of copper tape, it should come out to less than $1 per candle.
This first version of the candle doesn't flicker; it's really more like a little flashlight, but it's a nice shape and size to be used in lanterns or halloween pumpkins. I'm working on a design that uses a programmable ATTINY85 chip to flicker the LED.
Submitted by Ace Monster Toys Hackerspace in Oakland, CA for the Instructables Sponsorship Program
Step 1: Materials List and Tools. Also: What to Use If You Don't Have a Lasercutter
1 LED. I like the jumbo 10mm LEDS, for example this yellow one from Jameco.com
1 CR2032 battery, available from adafruit.com and at most DIY hardware stores
1/4" adhesive copper tape, you can find it on amazon (see below for alternatives)
A bamboo skewer or short 1/8" wooden dowel
A strong clamp (an office binder clamp works well)
What if you don't have a laser cutter?
You can cut these pieces out of 1/8" corrugated cardboard using a craft knife, or out of 1/8" wood using a scroll saw. You can even cut them out in layers of thin cardboard with scissors, and glue the layers together. if you choose a different material just pay close attention to the thickness of piece #2: It should be almost the same thickness as the battery. All of the parts need to be strong enough to hold up to use, and they need to be non-conductive, but if you keep those things in mind you can cut them out of anything you like.
Alternatives to copper tape
Since I was making a lot of these at Ace Monster Toys I bought a whole roll of 1/4" adhesive copper tape, but that's expensive. One alternative is to buy a smaller roll of copper tape from your local garden center - they sell it there as a snail deterrent. You'll need to cut it down into 1/4" strips. The simplest alternative of all is to use ordinary aluminum foil from your kitchen. Again, you'll need to cut it into strips, and you'll need to glue it. Rubber cement will work better for this than wood glue. Aluminum foil is thinner and more delicate than copper foil, so the key thing is not to leave any jagged edges that could tear as you move the switch arm.
Step 2: Apply the Copper Tape
Use your fingernail (or a friends fingernail, or something else that won't tear the metal foil) and push the metal foil gently into the slit at the top of piece #3. You can see this in the picture if you look closely. The idea is to make enough room for the 'leg' of the LED to fit into the slit and be in contact with the metal.
Step 4: Clamp the Pieces and the LED Together Without Glue
Slide your LED over part #2 with one leg on either side. The long leg, the + leg, should face up - towards piece #1 and the + side of the battery.
Stack the pieces face up with #3 on the bottom, #2, then #1. Clamp them together as shown here.
Before we go on to the next step, take a good look at your candle, particularly around the legs of the LED. The wood pieces should fit tightly against each other and the LED legs should be pressed into the slots at the top of pieces 2 and 3. If the legs of the LED are creating a gap between the wood pieces then the electrical contacts won't be good and the candle may not work. When I'm debugging (trying to fix) people's candles this is almost always where the problem is - so look at it carefully now and tweak it if needed.
Step 5: Insert the Battery and Switch Arm, and Test
Step 6: Glue, Clamp, Let It Dry
Let the glue dry for at least an hour (or follow the instructions on your glue).
Step 7: Finishing Steps
Put the battery in. Slide the switch arm into place and put the skewer or dowel through the hole. If it's too tight, sand it down until it fits snugly. Make sure the switch arm can move freely. Trim the dowel with the wire cutters.
If the dowel isn't tight enough to stay in place with friction, glue it to the outsides of the candle - but don't glue the dowel to the switch arm, you want that to stay moveable.