From my experimenting, which is not over by the way, I found that this simple excercise was the most revealing.
You will need a huge magnet like used in a wind power project. The rest is available through normal hardware store or RS. I'm sure a good sized speaker magnet would probably work if you have a sacrifice to make.
1 small spool magnet wire (about 30 feet of 24AWG)
1 bulb from or for a keychain flashlight (two refills for $1 around here)
1 Neodymium magnet 1inch x 2inch and 1half inch thick (about $10 plus shipping and any tax)
Step 1: Get wire off the spool and re-wind it
The idea is to expose as much wire to the highest concentration of magnetic field as possible without shorting the wire in the coil. This is why we use magnet wire. It isnt magic wire that makes electricity, it is just that magnet wire has a much thinner sheath and its usually made of enamel.
The extra thin sheath allows you to cram more wire in the same space as you would regular wire.
The attached mov file is my drill coil winding jig in action.