Take your enamlled wire and tape it to the outer paper, now carefully coil the wire around. Coil it until it's about a third of the way down, remember to keep the wire close together as you wrap it around. When you've gone far enough use another piece of sticky tape to secure into position. Give yourself plenty of wire for both connections of the coil, you can always trim these later if they are too long.
Once your copper coil is secured you can remove the inner paper tube and stack of magnets.