Never made one for beer, but similar for my grad research. Should be pretty easy. Find a smaller diameter bucket than your fermenter or something cylindrical that's similar. Leave several feet straight at the bottom (this will be bent up later) and begin wrapping the rest around the bucket working your way up. Once you've reached the desired height of coils, bend that end of tubing as well as the straight part from the bottom up using a beer bottle as a mandrel to not kink the tubing. Make any additional bends you'd like, but I'd probably use plastic flexible tubing (water line used for refrigerators or similar) to make my connection to the faucet and drain outlet. I personally prefer flange fittings from my experience with my research but doubt you'll be using liquid nitrogen that would cause the copper to contract and cause a compression fitting to fail.
Yup, no liquid nitrogen. I bought one of those spring pipebenders, and it sucks. Got a couple small kinks, but overall it went well. I wrapped it around a keg to get the coil size.
Still not sure if I'll use rubber hose and clamps, or get some hose fittings.