If you have a table saw, you set the blade to a depth of just a little less than the thickness of the wood. For example, if you use 3/4" cabinet grade ply (assuming it's really 3/4 exactly), set the blade to 11/16 or so, and place numerous cuts across the back of the wood vertically (in relation to how it will be when in position; perpendicular to the intended direction of curve). One cut about every inch like this will let it flex, and the more frequently you place the cuts the smoother the curve will be.
You could also try soaking the wood, laying the frame of the stand on it's back, laying the wood on top, and weighting it to slowly coax it into the proper shape, but I've never tried that so I have no idea how good it will work, especially with plywood. It'll probably take days or weeks and a lot of soaking.
BTW, expect to go through at least one piece to breakage!