Back when I was in college, I built a couple stands with just hand tools. got some 2x4's from the local lumber yard, walked them back to my dorm, cut them with a cheap miter like Kado posted (except lower quality), and screwed them together using a leatherman (that was the worst part).
If you build the stand properly, the screws shouldn't really be structural- they mostly just keep things aligned, and clamp it together while the glue sets.
Most of your big-box stores will cut wood, some have a certain cuts/piece limitation, others charge a certain amount per cut, it really varies. I don't think I've ever gotten a really accurate cut, I usually just get bigger pieces chopped down so they are easier to carry.
I think doing without a drill might be the hardest part, but that's still doable. And drills are fairly common, so maybe you can see about borrowing one from a friend or something. It might also be worth checking out some flea markets and such, sometimes you can find some old beatup hand tools pretty cheap, and a hand drill would be a major help.