Measure the width of the floor area where the box will be located. Cut two 2-by-4s to the width measurement; these are the width pieces.
Measure the length of the balcony floor space. Subtract 4 inches from the measurement. For example, if the area is 4 feet wide and 8 feet long, subtract 4 inches from the length to make it 7 feet 8 inches. Cut two 2-by-4s to this length; these are the length pieces.
Lay the two width pieces parallel along the width of the balcony flush against the wall and corners; stand the 2-by-4s up so that they are resting on the 2-inch side.
Place the length pieces against the wall along the length of the floor space so that the end grain, the cut ends, are in contact with the face grain of the width pieces.
Transport the lumber from the balcony to your work space keeping the 2-by-4s in the same rectangular arrangement. Drive two screws into each corner; drive the screws through the face grain of the width pieces and into the end grain of the length pieces.
Cut a sheet of plywood the width and length of the balcony floor space. If working with narrow plywood, cut the sheet in two sections. For example to cover a 10-by-8-foot floor, cut two 5-by-8-foot sheets.
Place the sheets on top of the 2-by-4 rectangle.
Drive screws along the perimeter of the plywood to fasten it to the 2-by-4s. Place a screw every 3 inches.
Attach the boring bit to the drill. Drill eight 1/4 inch holes in the plywood for every 1 square foot of space; these provide drainage. Scatter the holes across the sheet leaving 2 to 3 inches between each hole.
Cut a piece of shower liner 4 inches longer and wider than the floor area covered by the box.
Turn the box over so the plywood is on the bottom.
Lay the liner in the center of the box. Smooth the liner from the center toward the sides of the box, letting it bunch in the corners. Place a few staples along each side board to hold the liner in place on the sides.
Smooth the liner from the center of the box toward the corner. Hold the material down in the corner while you lift, tuck and fold the excess. Fold the excess material over to one side and staple it against the 2-by-4s to hold it in place.
Puncture the liner with an awl. Place holes over the holes in the plywood to facilitate drainage.
Move the grass container out to the porch and set it down.
Fill the container with turf or grow your own grass. Consider lining the base of the container with a 1-inch layer of gravel to facilitate drainage and prevent root rot.