I've been on a paracord buying spree and needed a storage solution; here are the sturdy, easy to make cardboard winders I've come up with.

I've been using the first one as a template so I can make them all pretty standard, but you'll see those existing cuts even in the first steps.

UPDATE: Added another picture of the paracord all wound and another step to demonstrate securing the loose end.

Supplies

Sharp knife or heavy-duty scissors
Corrugated cardboard
Wide packing tape

Step 1: Cardboard Panel

Start with a piece of cardboard twice as wide as the winder and fold like a book; I put any ink or printing on the inside so it won't rub off.

Step 2: Mark and Cut the "Wings"

Mark and cut angles for the sides; do not cut across the bottom. I roughly measured these with my thumb to make them more-or-less even - this isn't rocket surgery.

I use a box knife to cut through both layers at the same time so they match up - BE CAREFUL!

Step 3: Fold the Cutouts

Open and fold the extra pieces inside the "book" and tape the long edge tightly closed.

This adds some thickness to the middle of the winder which seems to make the whole thing much stiffer.

Step 4: Optional: Tuck the Cord In

For paracord, I tuck the end in between the folded tabs to start the winding; for something like extension cords or light strings, I wouldn't.

Step 5: Securing the Loose End

Finally, to secure the end I usually either tuck it between the layers at one end or the other.

I'm not sure if doing this on the taped edge (like the purple here) will start a split, so I've moved to making a small cut on the folded side (as shown with the green.)

For small string / thread, angled cuts on the folded edge work pretty well too, like in the second picture.