Stack two plywood pieces, 18 by 18 inches, 3/4-inch thick, one on top of the other. Drill 1/2-inch holes through the plywood pieces every 4 inches in a grid-like pattern.
Align the pieces next to one another, with a 1/4-inch gap between the sheets. Space two hinges evenly over the gap. Attach the hinges with screws to form a unit that can open and close like a book.
Place a drawer handle on the outside of one of the plywood pieces, along an edge opposite the screws. Secure the handle to the plywood with screws.
Lay a piece of folded clothing on the piece of plywood without the handle, and press the unit closed to wring out the clothing. Open the unit with the handle, and check for excess water. Press again as needed. Wring one piece of clothing at a time.
Use a 1/4-inch bit to drill 20 to 30 holes into the bottom of one of the laundry baskets.
Measure the diameter inside the bottom of the laundry basket. Measure and cut a piece of plywood into a circle with this diameter. Attach a drawer handle to one side of the plywood, if you desire.
Set the unaltered basket on a flat surface. Rest the two 6-inch boards inside the basket, spaced apart.
Place the laundry basket with the series of small holes inside the first basket on top of the boards. Place your wet clothes into the basket with small holes.
Push the plywood circle down onto the clothes to squeeze out the water and allow it to fall through the holes along the bottom and sides of the basket. Readjust the clothes, and press again until they are dry enough to hang.