Find the wall studs in the wall recess and mark their position at 20 inches around the recess. Mark a level line around the walls at this point as well.
Measure the length of the back wall of the recess and cut a length of 2-inch by 4-inch lumber to this length. Screw the 2-inch by 4-inch lumber to the back wall, just under the level line, through the stud points.
Measure the length of the side walls and cut four lengths of 2-inch by 4-inch lumber to this length, minus 6 inches. Attach two of these planks under the level line and two against the bottom of the wall, parallel with the ones under the level line but touching the floor. These are cleats, or supports, for the window seat.
Measure the open side of the wall recess and cut two lengths of 2-inch by 4-inch lumber to this measurement. Abut one plank onto the ends of the two side wall cleats and screw it in place through the side of the plank into the end of the side wall cleats. Attach the second plank in the same manner to the two cleats that touch the floor.
Measure the distance between the back wall cleat and the cleat over the open side of the recess. Cut two lengths of 2-inch by 4-inch lumber lumber to this length. Evenly space these two cross-supports between the back cleat and the cleat on the open side of the recess, and attach them with corner brackets and 3/4-inch screws.
Cut a piece of plywood that measures from the height of the support planks to the floor and the width of the wall recess. Place this panel over the front of the recess, and nail it in place through the front of the plywood into the upper and lower cleats.
Cut the paneling to the same size as the plywood and attach it with finishing nails to the front of the window seat. Cut a second piece of plywood --- for the lid of the window seat --- to fit the length and the width of the recess. If you want a lip on the lid, add 2 inches to the width.
Sand and paint the entire window seat, including the lid. Center the piano hinge over one side of the lid and screw it in place with 3/4-inch screws. Center the lid over the top of the window seat and screw the remaining portion onto the back wall cleat to finish the window seat set into the recessed wall.