If they had caps in TRON, this is what I think they might look like.
Step 1: Materials
EL Wire colour of your choice (around 2m)
AA battery Inverter
Thin clear fishing wire
Super Glue (Not shown)
AA Batteries (Rechargeables will work)
Snips (Not shown)
Step 2: Planning
Now this is 'Ible is for a cap but it can be applied to most head wear.
Figure out which parts of the cap you're going to light up and where you're going to route any wires extra EL wire etc...
For me my original plan was to go along up, back down the way I came and along all the way round. That was until I found that for this thickness wire it would only bend about 4/6 of the way on itself, so I came up with the layout you see above.
I hid the run from the back to the front to light up the rim on the inside of the seam and at the back put a bit of heat shrink on to make it symmetrical.