With Ditto, you can potentially use the process without a machine by dampening the paper with alcohol, and pressing it against the master. I did this years back, just to see if it would work. No guarantees it'll always work--all I can say for sure is that it worked the time I tried it. Plus, I suspect that a machine would probably work better and have longer master life. But it was an interesting experiment.
With Mimeograph, it's worth noting that--as I understand it--it not only uses ink, but the master is actually a stencil. Advantage is much better life. I'm not sure what Ditto can do--I suppose it depends on the master brand, how it's run off, etc--but a hundred copies or so is probably the best you can hope for. But Mimeograph was apparently harder to correct, and I was told it could be quite messy. My memory from school was that Mimeograph was always handled by a secretary, possibly because of the mess, but teachers would use the Ditto machines themselves.
And Mike, if you think your old teacher was shocked by your news, try telling someone who is too young to remember when Ditto was king. Back in the 90s, I wanted to run something off for a bunch of people who'd remember the technology. I remembered a local college library that a Ditto machine only a few years before. It was, as I best recalled, available for public use. Figuring that they might still have the machine, I stopped by one night and asked. The 20 or so year old clerk had never heard of the machine. I explained the technology. He said they had nothing like that anymore. Then he started asking me questions if the thing actually worked, and if it wasn't horribly slow. I left that question and answer session feeling old!