Potatoes and onions both keep the best under similar conditions: Cool, dark and dry, with air circulation. The same sort of bin will store either potato or onion storage crops equally well, but you should store each food product individually. Make one bin for potatoes and another, if you so desire, for onions. These plans are for a slatted storage bin that is two feet by three feet by two feet, and can be easily modified as necessary to create a larger or smaller bin.
Start building your potato & onion bin by laying two of the 1-inch-by-2-inch-by-34-inch boards out on edge, parallel to each other, with about two feet between them. Place one of the 1-inch-by-2-inch-by-24-inch boards on each side of the two longer boards, forming a box with the longer boards sandwiched between the shorter board end pieces.
Hammer at least two nails through each end of the shorter boards into the longer boards, holding the corners of the box together.
Place the plywood sheet on top of the open rectangular box you just made. It should line up perfectly. Hammer nails down through the corners of the plywood into the boards, then along the sides of the plywood at six-inch intervals, to hold it against the boards.
Turn the plywood over so that the boards are facing up. This is the base of your slatted potato & onion bin.
Stand four of the 1-inch-by-2-inch-by-24-inch boards on end inside the rudimentary bin you've created. Snug them up against the sides of the bin, one in each corner. Hammer nails through them into the boards that make up the sides of the bin. These will support the walls of your slatted bin. Then lay the bin on its side to make the next step easier.
Build up the sides of your box by nailing 1-inch-by-2-inch boards in place up the four supports you just installed, with one inch of air space between each set of two boards. You should be able to place seven more 1-inch-by-2-inch-by-34-inch boards on each of the long sides of the box and seven more 1-inch-by-2-inch-by-24-inch boards on the shorter sides of the box. Once you've nailed all the boards securely to the supports, you're done.
Place the bin, plywood-down, in a cool, dark place where you intend to store your potatoes and onions. It'll be too heavy to move easily once it's filled.