Measure the length and width of one of your cushions, or note the dimensions if they were available at the store from which you purchased them. You can also check the store's website, catalog, or the cushions' tags for the dimensions. Disregard information about the cushions' height, which is irrelevant for this project.
Cut your plywood to match the length and width dimensions of your cushions. Since the cushions will rest on top of the plywood, it's important that the dimensions match. Sand smooth any rough edges from cutting. If you'd prefer not to cut the plywood yourself, take it to a home supply store where they can cut it for you for a small fee.
Paint your cut board to match your cushions, or cover it with a varnish if you'd rather not paint. Allow the board's surfaces to completely dry.
Place your casters against each corner of the board and mark the locations of the screw holes with a pencil. Bore pilot holes into the locations you marked. Use a drill bit that is slightly smaller than the diameter of your casters' included screws.
Attach the casters to the painted, pre-drilled plywood board using the hardware that came with them. Flip the board onto its wheels.
Attach one-half of four lengths of peel-and-stick hook-and-eye fasteners along the each of the board's edges. Attach the other half of those sticky fasteners to matching edges on the underside of one of your box cushions. Hook-and-eye fasteners will help keep the cushions from sliding off the board.
Arrange your floor cushions so that the fastener-attached cushion rests flat on the board with the cushion's and the board's edges meeting. The fastener strips will grip to each other. Rest the remaining cushion or cushions on top with all edges matched. If you want a low foot ottoman, use only two cushions, and increase as desired.