Step 1: About EL wire
EL wire is thin and flexible, can be bent, wrapped or even sewn into clothing. It runs off of high-voltage, low-current, high-frequency AC, which is typically supplied by a battery pack with an inverter, also sold by the same companies. EL wire will eventually "burn out", depending on how hard you drive it. The wire itself has a central core coated with phospor, wrapped with two very tiny "corona wires".
My EL wire came in convenient 6-foot lengths from CooLight.com; each length came pre-soldered with a connector at one end and a non-conducting alligator clip at the other for securing the "tail" end of the wire to anything handy. EL wire can be soldered, it's a little tricky, but there are some good instructions here. The connectors can be any basic 2-conductor variety. Locking, hooded connectors are probably best, to reduce the risk of accidental shock. I got the connectors from CooLight, but it looks like these connectors from AllElectronics.com are pretty much the same thing.