Precreasing cleanly (without unnecessary grid lines) is quite straightforward. Start by precreasing both diagonals of the square. Then, fold creases parallel to the sides of the square at half the distance between the edge and the square’s center, creasing only the segment which lies between the diagonals. Repeat on each side. Then, make the creases denser by folding halfway between the crease from previous step and the edge and between it and the center. Continue to get as fine a division as needed (already a division into 32nds results in a pretty smooth hypar).