It's actually pretty easy to make papyrus. You need a lot of river
reeds (papyrus would, of course, be ideal, but you can get the idea
with other wide grasses, since papyrus doesn't grow everywhere). You weave
them together as if you were making a placemat, about half the size
of a placemat. You'll need a way to anchor the vertical reeds while
you weave them - a clipboard would do it. Then you pound the mat flat
with a rock or a hammer. Flip it over and pound the other side flat.
Let it dry (you can hang them on a clothesline with clothespins) until
it is not green anymore but all brown and dry. To make a bigger piece,
the Egyptians glued two pieces together.
You could also (and a lot easier) do this with strips of paper about 1/2 inch (1 cm) wide and 11 inches long or so. After you weave them, soak the mat in water before you pound it flat on both sides and let it dry.