Measure the wheelbarrow you want to use the sifter with. Remember that the lumber you're using is usually 1 1/2 inches thick, so allow for that when you're doing the math. For example, if your wheelbarrow is 24 inches wide, shorter cross-pieces of lumber are only 21 inches in length.
Cut two pieces of 2 X 4 lumber the length of your wheelbarrow, and two more for crosspieces that are the width of your wheelbarrow, minus three inches. Mark a line 3/4 inches from the end of each piece, and drill three holes for screws. This helps prevent the wood from splitting.
Construct the frame by screwing the four sections of 2 X 4 together, using 3- to 3 1/2-inch wood screws. Measure your wire mesh, available from the hardware store, to fit the box. Allow an extra two inches to help stretch the mesh, and cut it with tin snips or wire cutters.
Staple one side of the mesh to your box, using a staple gun. Stretch the other side by putting a long-handled screwdriver through the mesh on the middle of the overhanging side, and using that as a lever to pull the mesh. Staple it in place, move two inches in either direction, and repeat until the entire second side is secured. Staple the ends in place.
Cut four pieces of 2 X 2 lumber to the same lengths as the 2 X 4s in your frame. Drill screw holes in these, five each in the long pieces and three in the short pieces. Screw these to the bottom of your frame to hold the screening firmly in place.
To keep the sifter from sliding off the wheelbarrow, cut two pieces of 1 X 4 lumber the same length as your longer side pieces of 2 X 4. Pre-drill these with four vertical pairs of holes, and screw them to the sides of the sifter. The box now sits on top of the wheelbarrow and slide front to back, but not side to side.
Shovel dirt into the sifter, two to four shovels at a time depending on the size of your sifter and wheelbarrow. Shake the sifter front to back, or force the soil through with a trowel or gloved hand. The sifted dirt falls into the wheelbarrow, and stones or large pieces of compost can be tipped out when you are finished.