Gypsum is easy. You can scratch it with your fingernail. It is also typically translucent rather than transparent and usually has a subvitreous luster that may be waxy, silky, or pearly. If you have a hardness set, you can test hardness to distinguish between quartz and diamond. If you have another piece of quartz, you can use that to test hardness. Two quartz crystals rubbed together will not or just barely scratch each other. Diamond will make deep scratches on quartz.
well, about 90% of the time, I could tell just by looking at them, so the first thing I would do is look at them (which is what I do with every single mineral or rock). Then (or as part of that first look, really, not that it is consciously done) I would look at crystal form (if it was apparent) and then hardness. If I couldn't tell those three apart after a scratch test, I would be a pretty crappy geologist. But I don't need to scratch every single mineral specimen I see. The gypsum will pretty well stand out from the other two in almost every case. Diamond and quartz can have similar crystal forms (especially when the quartz is tiny), but hardness would be the decider if that was necessary. About all the three have in common is a possibility of being white in color.
Try to scratch the samples with each other.
