If you haven't already, cut the fabric squares to the appropriate size. Also, prepare kids for sewing by teaching them the running stitch on scrap fabric.
After threading needle (or teaching your child to thread the needle), sew the 2x2-inch square to the 3x3-inch square using the running stitch. Be sure to leave the top edge un-sewn to form a pocket.
Next, use the same running stitch to sew the 3x3-inch square to the middle of one of the 4x4-inch squares, again leaving the top edge unsewn to form a pocket.
With right sides of fabric facing each other (so that the pockets are facing inward), sew the two 4x4-inch squares together, leaving a small portion of one edge unsewn so the pillow can be turned inside out. Once the pillow is sewn, turn pillow inside out and stuff with filling. Sew the pillow closed.