It is not easy, but you can get inside by removing the outer case and the glass:

What you find inside is a stylus mounted on a pair of orthogonal rails. These rails move when you turn the knobs. Also inside is a mixture of extremely fine aluminum powder and beads. The beads help the powder to flow evenly.

When you turn the Etch-a-Sketch upside down and shake, it coats the inside face of the glass with aluminum powder:

“Why does the aluminum powder stick to the glass?”

After you play with the powder, you know that the answer is, “Because it sticks to EVERYTHING!”

It is amazing stuff!

tightly strung and very thin steel wire that connects the knobs to the horizontal and vertical bars through a pretty complicated pulley system. The wires connect both ends of each bar to its respective knob

When you turn a knob, it moves its bar, and this moves the stylus. The stylus scratches off the aluminum dust coating the glass to create a line on the screen. Read more at www.howstuffworks.com