The frame is made out of some scrap 4x4s and 2x4s, the plunger out of 1" pine board and plywood (just because I ran out of pine), and the screw is from a bench vise. To attach the plunger head, I drilled and tapped a 1/4" hole in the end of the screw vise, and bolted it on. After some use, I've found that it's best if you cut the bolt that holds the plunger on so that it bottoms out in the hole, that way you can tighten it without sinking the bolt head or washer into the soft pine board when you start pressing cider. The bucket is a cheap ice cream maker bucket with a small hole drilled in the side and a spigot made out of some hardwood scraps glued on. I sealed all of the parts of the wood that come into contact with the cider with a couple coats of Howard's butcher block conditioner.
Eventually, I will upgrade the cheap plywood and pine plunger to a better hardwood one, probably oak, but for now, this one works just fine.
When I got ready to start pressing, I quartered the apples and ground them up with a meat grinder, which I must say worked incredibly well. I bought 2 yards of tulle to use as the press cloth; lining the bucket with it, I slopped in several ladle-fulls of the ground up apples and folded the tulle over it, then pressed away. The one main problem with this design I found is that since there is only one hole for the cider to run out through, I had to tip the press as I was tightening it to get all the liquid out. Other than that, no problems, only delicious fresh cider!