Copper tape comes in a few widths and thicknesses. We tried 2 different widths, 1/4" and 1/2". Make sure that the tape has a conductive adhesive so the circuits will be properly connected.
LEDs come in many sizes, colors, and brightnesses. Some of the websites about paper circuits use surface-mount LEDs and a soldering iron, but we used standard LEDs: 5mm with 2 "legs" (the anode: the longer + connection; and the cathode: the shorter - connection), and Scotch tape. If you want to try a few different kinds of LEDs out before ordering a large amount online, Radio Shack has them individually or in small packs.
For batteries, look for 3v coin cells. There are a few sizes available, but as long as it's 3v, you're good to go! If you have some of the very small 1.5v coin cells, you may use 2 of them to light up the LED. I do not recommend the smaller 1.5v batteries, as their squat size makes them difficult to keep stacked when making the circuit connection.
This workshop is mostly based off of Jie Qi's instructions from her website. She has clear instructions and printable templates for many types of paper circuits.
A basic internet search for "paper circuits" will yield a number of results using various methods and materials. I've included a few links using soft graphite pencils (found in the fine art section of craft stores) instead of copper tape. I have not tested this method, but feel free to give it a shot!
These links are to remind you how to make the circuits and to offer inspiration for your own projects! Try wiring up origami, greeting cards, or old books. Experiment and have fun!