Step 1: Start With a Piece of Paper
Fold into eighths along the long direction.
Then fold 14 diagonals in the opposite direction, using the ends of the first folds as guides.
I made poor creases on the first try (they didn't align with the edges of the first set of creases), but then had much better success using a pencil and a straightedge.
Step 2: Taking Shape
Finish the barrel by encouraging the folds so that the paper curls into a half-circle.
Eventually, it will fold up accordion style into a flat, rotationally symmetric 2D shape.
Awesome thin shell concrete roof: