Measure and cut out three 12-by-24-inch rectangles from your plywood sheet.
Place the three rectangles on top of each other, so they lay even (like a deck of cards). Sketch a curve on the rectangle that is on top. The steeper the curve, the higher the ramp.
Cut each board the same with a jigsaw, following along the curved line. You should now have three curved boards that will be used for your vertical supports. These supports will hold the deck of the ramp.
Measure and mark three different places on one vertical support board--one at top, one in the middle and one down below. Mark the other two boards in the same way, making sure to measure so all points add up. These spots are for the horizontal support beams that connect the three vertical supports.
Cut your 10-foot 2-by-4 board into three 30-inch pieces. These will be your cross beams.
Trace the end of one of your cross beams onto a curved vertical board that you previously marked. This will give you an exact outline of your beams. Cut slots the size of your 2-by-4 horizontal beams so they will lay snug inside each slot. Connect the vertical curved boards with the 30-inch 2-by-4 boards, placing the 30-inch boards inside the slots.
Cut your plywood board with either a hand saw or circular saw to measure 30-by-30 inches.
Score the back of your 30-by-30 cut plywood with a utility knife. Each score should be 1/8 inches deep and spaced 1 to 1 1/2 inches. This will help your plywood bend more easily to the curve of your vertical support beams.
Place the scored plywood board onto your vertical support structure, with the scored side down, and screw with 1-inch screws into the horizontal beams. You should put three screws going across the top, three going across the middle and three going across the bottom.
Cut a 34-by-34-inch piece of plywood. This will be for the base of the ramp.
Flip the ramp over and attach the base to the bottom of the ramp using 1-inch screws. Make sure that the back of the ramp sticks out 8 inches more than the front. This will keep the ramp from tipping over.