How Do I Build a Faraday Cage?

I would try to attract an African Grey Parrot to your cage as they are the "High end" in talking birds. Sorry I can't help with the Faraday cage, but I'm hoping to learn more on this post. I did look at your Funhouse though and I'll bet you have an exceptional sound. I especially like the rack you built to hold your system.

Check out Verastarr.com for their "StarrDamp CS" sheets as one approach to reducing cabinet resonance while simultaneously shielding against RFI.
For interconnects, check out Zcable.com for their "Z-Sleeves". They have already designed and built what you want.
I use one surrounding the IC from turntable to phono RCA input, and one surrounding the older, fixed, power cord of my turntable, with resulting audible benefits as mentioned on the Zcable,com website.
If one places one of the tubular Z-Sleeves right in front of a squawking parrot, or Audiogon member like myself, furiously typing away, there is an immediate sweetening or mellowing of the noisy output from either one :>)

To see if you really want to do this, wrap the thing in Reynolds Wrap (Aluminum foil) and ground the foil. If this makes no difference spend the money you save on good recordings.

I remember using one when I was a grad student doing open and closed cell patch clamping. Absolutely could not do without a cage, to much interference. I am sorry though, it was built when I got there. You might try contacting a university that has a neuroscience graduate program. Might even be able to higher a poor underpaid starving grad student to build one.

If you do a search on ask.com or the like you'll find a lot of information on construction, resources, etc. But as was said before it is basically a box made of conductive material that is grounded separately from your components. They're used to protect devices from outside RFI/EMI getting in, or inside RFI/EMI getting out.

Cheers,
Tom