Learn to Spin
If you want to check out spinning for yourself, start by spinning some long grass on your own leg. Just pick some long grass (at least six inches makes it easier), take five or six blades and lay them side by side, then use the flat palm of your hand to roll them up and down your thigh or your shin, until they get twisted together (works better on bare skin, like if you have shorts on). Now you have a short string. To make it longer, take another small bunch of grass, lay it on your leg next to the first one so that they overlap by a couple of inches, and roll the place where they overlap until they twist together. You can keep doing that to make your string as long as you need it.
Some things to check out: does it make any difference if you always roll in the same direction or back and forth? Does it make any difference how many blades of grass you use? Do different kinds of plants work differently? How about your hair? What other kinds of fiber might you use? (dog hair? stems of ivy? cotton bolls? sheep's wool?).
To try spindle spinning, you can make a pretty fair spindle with a pencil and a radish or a small potato. Stab the pencil through a small potato so a little of the pointy end comes out the other side. Take some fiber you have already twisted up (the cotton batting for stuffing toy animals works) and tie one end to your spindle (just on top of the potato).
You Can Weave!: Projects for Young Weavers, by Kathleen Monaghan (2001).
World Textiles: A Concise History, by Mary Schoeser (2003). For adults.
Women's Work: The First 20,000 Years : Women, Cloth, and Society in Early Times, by Elizabeth Wayland Barber (1995). Not for kids, but an interested high schooler could read it. Fascinating ideas about the way people made cloth in ancient times, and why it was that way.