Google tells me that this is the Giant Upland Ladies':



Those parts are good enough that, if you really wanted to learn about bikes, you could move them all over for a satisfying project. If you're mechanically inclined, expect it to be a couple of weekends if you haven't done it before. My guess is that if you find an aluminum framed bike at a tag sale or something (it's the season, after all) you could swap over the parts you want.

If you're not mechanically inclined, you could learn a lot by doing this, but be prepared to have to learn a whole lot of stuff.

Either way, you'll have to buy a bunch of bike-specific tools and perhaps non-bike-specific tools if you don't have them. If you want to build a bike (and do it again sometime), it's a great investment. If you just want to ride, it'll be more cost effective to have someone else build it — that is, buy a new one.

(I helped my brother swap parts to a new frame and it took about 2 1/2 hours, including filing some parts to fit differing 1960s standards. We had all the tools we needed, though, and I'd already built a couple of bikes.)