This is to help some friends who want to add simple lights to some costume parts (hats, etc.). The real answer depends on time and resources. There are many options so here are a few from simple to crazy. This is for them, but if others get something out of it then that's terrific.

I tried to keep the simpler options to materials you can find in most hardware stores like OSH, HD, Lowe's, etc. in case you are in a hurry and can't wait for shipping or don't have access to an electronics part store like Fry's.

(All images created in Fritzing.)

Step 1: Parts

You will need:

an LED
- Best: 5mm or larger diffused red/green/whatever, or
- cover a white one with translucent plastic
- Look for the type called "super bright" if possible but you may need more or bigger batteries
- LEDs are everywhere so you may be able to scrounge one out of a flashlight or something. You need to be able to get at the leads, so this might be tricky unless you have a soldering iron.
- You don't have to use an LED, a regular bulb of the right size like a flashlight will work, but LEDs are bright, cheap, and use very little power.
a battery
- a 3V coin/button type, small but can run out more quickly
- 2 AA or AAA 1.5v wired together, the plus terminal of one to the minus terminal of the other
- 9V -- but a 9V might be hard on some smaller LEDs, use a resistor with this!! (see below). This could be a good option when wiring a bunch together (see later steps).
- pretty much any other 3V - 6V 'specialty' battery for various devices
- Higher intensity LEDs may require more voltage and/or amperage
a switch
- momentary push button like a doorbell
wire (24 gauge speaker wire is the biggest you should use, try to get more like 30 gauge)
OPTIONAL: A small resistor (1/4 watt is good). The size depends on a lot of things but here (one standard LED) it's mostly the voltage: 56 Ohms for 3V, 220 Ohms for 6V, or 390 Ohms for 9V.

Nite-Ize makes an "upgrade" kit for Mini Maglight flashlights. It includes a white LED with a reflector and a pushbutton switch. You could cannibalize this for the parts but the LED is pretty small, so your milage may vary.

Step 2: Wiring

You need to hook it up like this (see top image): one lead of the lamp -> wire -> one switch terminal ... other switch terminal -> wire -> one of the battery battery terminals ... other battery terminal -> wire -> other lead of the lamp.

The best connection is to use solder. Lacking that you can twist the wire tightly and wrap in electrical tape but it may come loose so be careful!

IMPORTANT: the LED only works in one direction! If it does not light up you need to turn it around. Hint: The longer lead if there is one should go towards the the positive (+) battery terminal. If there is flat side near the bottom it should go towards the negative (-) battery terminal.

Step 3: Optional Resistor

The resistor will keep too much current from flowing through the LED which will make it last longer. Some people will tell you it's necessary but today's LEDs are a lot tougher than they used to be.

There are many opinions on where in the circuit it should go, but in my experience it's on either of the LED leads.

Step 4: More LEDs

More LEDS in the same circuit could look good but each will eat some of the power and will either eat up the battery faster or they all will be less bright.

Parallel: Hook all the positive leads together and all the negative leads together, and hook all those into the circuit.

Serial: Hook the positive of one LED into the circuit as above. Hook its the negative lead to the positive of the next, and repeat like a chain as needed. Hook the negative of the last LED into the rest of the circuit.

Play with these and see what works for you.

Step 5: And Beyond...

This can get really crazy. The video is something I made last year with SuperBright LEDs, pushbutton switches, resistors, and AdaFruit ProtoBoard, and an ATTiny85 microcontroller.