In Illustrator, using pure color shapes (100% cyan, 100% magenta, etc.) what’s the best method to overlay them so this effect is obtain (colors blend together, instead on merely being added one on top of the other, and a CMYK offset effect is created). Should I use multiply, but with all the shapes in the same folder?
If you just want to do it visually then just set the transparency to multiply as you've figured out. You can just set everything at once without worrying about folders.
If you want the black look like it's mixing, make sure you're not using a rich black (i.e. one with CMY components). You may want to lighten the black a bit to enhance the effect.
If you want to actually have inks mix when printing, which is called overprinting, you need to set that using the attributes panel. But you won't see the effect right away. You have to go to view->overprint preview.