After a bit of searching, I found a good set of instructions from instructables. Instructables is a cool website that people upload directions on how to do just about anything. It's up there on my list with reddit and StumbleUpon for sites that teach you random interesting things. Slash waste tons of time.
Anyway, once I found the instructions, I had to find a LOT of cheap apples. I found a farm stand in the Eastern Townships that was selling 20 pounds of deer apples for $5, so I filled my car with those. Since they were ground apples, some were getting kind of gross, but after a quick pick through them, I brought them back to the city.

The next day, we had to juice all the apples. We borrowed a friend's juicer, and Lacey spent hours and hours sticking hundreds of apple pieces in the tiny juicer. Worse, there was still lots of juice left in the pulp, so we had to use a (clean!) pillowcase to strain the applesauce to get more juice.
It would have been much better if we had dedicated an entire Saturday or Sunday to do this project, but instead we broke it up into several evenings during the week. Either way, it felt good when we finally had about 16 gallons of apple juice.
After a few days, the cider started to bubble as it fermented. Within about a week and a half, the bubbling stopped, and we knew it was time to separate the cloudy apple bits which settled out on the bottom.

The instructions recommend that you leave the cider to age in a cool, dark place for another few weeks.

Will I do this again next year?
....maybe.
I would definitely try to use a cider press to cut out of the mind-numbing cutting/peeling/juicing part, or I would use apple juice from a farmers market and skip all of those steps entirely. But, this fall's project has been fairly successful and I have some cider to drink!