You can manually agitate the paper in a jar with pebbles or pennies to break it down, though it takes much longer.
Tear your paper into small bits (about 1 inch) and soak them in warm water for at least 30 minutes, or overnight for tougher materials like cardboard.
Fill a blender halfway with warm water and add a handful of soaked scraps. Blend until the mixture looks like a thick, soupy slurry.
Carefully flip the screen over onto a damp cloth. Press down firmly to transfer the wet sheet of pulp onto the fabric.