Sturdy, lightweight and cheap, cardboard is craft material that is hard to beat. Corrugated cardboard is made up of three layers: a sheet of wavy "fluted" paper in soft vertical accordion pleats sandwiched between two smooth layers of paper. Whether you use cardboard to provide hidden strength to a project like a book cover or as a project's surface material, it likely needs to be bent or folded. Because the material is designed to be stiff, a clean bend or fold can be difficult to achieve.
Lay your piece of cardboard on a hard work surface. Look at its edges. If you can see the wavy line of the fluted core of the cardboard, you can cleanly bend or roll the cardboard in the same direction as the fluted material. You should be able to see little lines or ridges running along the surface of the cardboard. This is called its "grain."
Mark with a pencil or pen along the line where you want to bend the cardboard and fold along the line. The cardboard will easily fold along the fluted ridges in its core.
Line up your piece of cardboard so its grain is parallel to the edge of your work surface. Run the cardboard over the edge of a table, pushing down slightly along its length to crease the paper between each fluted ridge. You will now be able to roll the cardboard into a cylinder or bend it into an arch or "U" shape.
Lay your cardboard on your work surface. Make sure it is a solid, stable table or countertop.
Draw your pattern on the wrong side of the cardboard, marking any fold lines. Lines may go directly perpendicular to the grain or diagonal to the grain at any angle.
Line up your metal or metal-edged ruler along your fold line. Press the edge of the ruler firmly down into the cardboard. Lift up the ruler, move it down the line and press again if your fold line is longer than the ruler. The ruler will leave a groove in the cardboard without breaking its surface. The cardboard will now bend easily along the groove.