Reddit mentions of The New Sewing Essentials (Singer Sewing Reference Library)

Dude, I was where you are a few years ago. I decided to learn to sew for similar reasons. I bought a mint 1954 Singer 15-91 for $25 off of Craigslist...the beast can even sew leather! If you find you like sewing, the old machines are worth a serious look.

I suggest going to the Goodwill Store, DAV, Salvation Army Store, etc. to get your hands on patterns for practice. You'll be surprised how many cheap patterns are usually there. You'll find all sorts of other stuff too, thread, needles, embroidery/darning hoops, machines, mannequins, and cheap garments to disassemble for use as templates! While you are there look for bed linen as a cheap bulk practice fabric. You'll not find fabric so cheap anywhere else. (first pair of lounge pants I made were from a gray flannel sheet that cost me fifteen cents!) Also, don't forget garage sales...so many deals on the cheap!

Other than that, use Google as your resource, and practice sewing. Oh, I did buy a new $6 book at a used book store: Singer (the new) Sewing Essentials It's has been extremely helpful to me as a noob.

I'd like to start by saying you don't have to be aware of all the technical aspects of fashion design to show her you're supportive and interested in what she's going to do with her life. Listening to her when she tells you about a project, commenting insightfully on her work when she shares it with you, and being there for her when the work load is particularly overwhelming (because, trust me, it will be at some point or another) are the most important things you could ever do to show you care.

As for technical terms, pick up a beginner's sewing book, like Singer's The New Sewing Essentials. Since fashion design has been getting more attention as a glamorous career, there are a wealth of small "crash course" type books that can teach you the basics about textiles, fashion history, marketing, creative direction, etc.