I was wandering around in Powell's Books, and took a look in the luthier section. The "real" guitar books were totally overwhelming, but there was this: "Pickin' Stick: Building a Stringed Instrument" by John Ressler. I flipped through it and looked at the little guitar-looking things on the cover and bought it. (Amazon Link) The book seems perfectly suited to a high-school woodshop class project. There is plenty of detail in terms of building the instrument, although I quibble a bit with some of the parts suggested. There are plenty of tuning machines that come in sets of three, for example, but he tells you to get a four-machine set and cut one off. Weird. There is also almost no discussion of theory, in terms of construction or of playing, so if you're ignorant like me, you'll be looking elsewhere for that information. Fortunately there's a ton of it on the web.
I picked up the necessary wood when I was in Crosscut getting some oak for my TV stand project, and built the little "pickin' stick" in between other things. It took me maybe three or four hours, and I think it turned out pretty well, although I did lose control while climb-cutting the back on the router table, so there's a minor defect there. Cost-wise, it couldn't have been much cheaper. I bought enough rough-cut walnut (body), maple (sound box back), and spruce (sound box front) stock to make at least four of them for $15, and enough hardware (from Stewart-Macdonald) to build two for another $20. By the way, here's what I ordered from Stew-Mac, with prices as of January 2011:
0148 Medium Fretwire - 2ft piece $3.17
0765 Stewart-MacDonald Mandolin Strings $5.98
0934 Economy 3-on-plate Tuner Nickel $9.28
There are several names for this instrument out there. It looks like some of them have maybe been trademarked, but "stick dulcimer" seems to be in the public domain, and makes the most sense to me anyway after researching a bit. It's got three strings and a fret layout like a mountain dulcimer, but built with a tiny little sound box. It's tuned the same, has the same physical layout, and can use all the same sheet music and cheat sheets.