Find the widest newspaper you can. Take two full pages and fold them over so you have four plies. Lay the paper on a hard surface with the fold at the top.
Take hold of the upper left and right corners and fold them in until they meet in the center of the paper. It's all right if they don't meet exactly. Crease firmly. Notice that you have created a triangle.
From the open edge at the bottom, fold just one ply up to the base of the triangle and crease. Fold it again, as far as it will go, and crease once more.
Turn the hat over, making sure the pointy part is at the top. Smooth all edges.
Grab the left and right edges. Bring them toward the center and overlap. The degree of overlap will determine size of the hat; more for small and less for large. You can skip overlapping entirely but it will make it more difficult to construct the rest of the hat.
Fold the lower right and left corners up to the bottom of the hat band and crease. Continue creasing all edges as you proceed. This will help keep the lines clean.
Bring the entire bottom piece to above the hat band and tuck it into the band. This forms the brim of your hat.
Take the peak at the top and tuck it into the brim. Crease crisply. Apply a dab of glue if peak is reluctant to stay in place.
Pick up the hat and lay it down with the brim up. Slowly pull the sides open and flatten the hat into a diamond shape. Smooth it out.
Tuck the corners into the brim. Open the hat, crease corners, and shape gently into a square. Wear with pride.