Return the large stuff to the compost pile, where it will continue to break down. Size the sifter to fit over your wheelbarrow or just prop one end up and sift right onto the ground.
You’ll need about 10 ft. of 1x6 lumber for the sides and another 10 ft. of 1x2 to clamp the screen to the bottom for the bottom screen molding. The lumber species doesn’t matter, but cedar will last longer than untreated pine. Buy a 24-in. x 36-in. piece of 1/4-in. hardware cloth and cut it with a tin snips to cover the bottom of the completed frame.

Click image to enlarge.
1. Cut two 36-in. lengths and two 22-1/2 in. lengths of 1x6 pine. Drill 5/32-in. clearance holes 3/8 in. from
the ends of the 36-in. boards and screw the corners together with 2-in. deck screws to form the sifter frame. Cut a piece of 1/4-in. hardware cloth to fit and staple it to the bottom of the box. Cut two 37-in. pieces and two 22-in. pieces of 1x2. Drill clearance holes and screw them to the bottom. Overhang the 1x2s 1/2 in. to cover any sharp edges of screen that may be sticking out.