Tin foil hat territory? Well, actually, it's baseball cap territory as the kit can sit in a peaked hat.
Check out the full steps on WikiHow.com.
They begin with wiring up the LEDs that will provide the flash-blinding light source:
Make sure your wires are long enough (around 15cm / 6 in each) depending on how big your hat is. Start wiring up the LEDs one by one, making sure to note the positive and negative terminals. (Color-coding the wires is highly recommended: for example, you can use a white wire for each positive terminal and a colour wires for each negative terminal.) Wrap the wires tightly to each LED so they won't fall apart. You can even solder the connections, though it's probably not necessary.
It's all powered by a standard 9v battery that sits within the cap.
What do you think? I at first expected the lighting to be triggered automatically somehow, but it seems the "invisble" IR lights will just always be on. I think you would have to be pretty paranoid to wear this hat all the time, with the battery being constantly drained (though you could have an on/off switch), just in case you are covertly recorded... Hmmm. It also strikes me that you would hide your face but you would also broadcast to CCTV that here is someone walking along the street who is hiding their face!...