Measure the width, length and height of the patio cushions. If you have a chair that has both a seat and a back cushion, measure the dimensions of both cushions.
Cut two rectangles of fabric that measure the width of the seat cushion plus an inch for seam allowance by the length of the seat cushion plus an inch for seam allowance, long. For a 20-inch-by-20-inch cushion, cut two 21-inch-by-21-inch panels. Cut two panels of fabric that measure the height of the cushion plus an inch for seam allowance, by the width plus the length of the cushion, plus an inch for seam allowance. These will be the sides of the cushion. For a 4-inch-high cushion that is 20 inches square, cut two 5-inch-by-41-inch panels. If your chair also has a back cushion, cut two squares of fabric that measure the width of the back cushion plus 1 inch for seam allowance in width by the length plus 1 inch for seam allowance long. Also cut two panels of fabric that measure the height of the back cushion plus an inch for seam allowance, by the width plus the length, plus an inch for seam allowance, of the back cushion.
Cut a piece of fabric for the hinge between the seat and back cushions, if needed. You can skip this step if your chair only has a seat cushion. The hinge fabric should measure the length of the seat cushion by 6 inches.
Cut the foam so that it is the same size as the cushions you are replacing. Use the electric knife to cut the foam. Cut a square of upholstery batting to cover the top of the foam. You can just drape the batting over the foam, as the cushion cover will hold it in place.
Place the two long fabric panels for the sides of the cushion on top of each other. Pin together along one short side, then sew. Repeat with the two long fabric panels for the sides of the back cushion, if necessary.
Drape a rectangle of fabric over the top of the seat foam, right side facing down. Wrap the side fabric around the sides of the foam, wrong side facing out. Pin three edges of the fabric on top of the foam to three sides of the fabric on the sides of the foam.
Turn the foam cushion upside down and drape the other rectangle of fabric over the bottom of the cushion, right side facing down. Pin the rectangle of fabric to the edges of three sides of the fabric around the cushion's side. Carefully slide the fabric off the foam cushion. Repeat with the back cushion, if necessary.
Sew the fabric together along the pinned edges. Repeat with the back cushion.
Slide the foam cushion and batting into the opening on the fabric squares. Repeat with the back cushion.
Pin the open sides of the fabric together. Hand sew the open part of the cushion closed, using a slip stitch. Repeat with the back cushion. If you only have a seat cushion, slide it onto the chair, as you're finished at this point.
Fold the hinge fabric in half lengthwise, right sides facing in. Pin on the long side, then stitch along the long side and one short side. Turn the fabric right side out and hand sew the other short side closed.
Place back edge of the seat cushion against the bottom edge of the back cushion, if using. Place one long edge of the hinge fabric against the back edge of the seat cushion and pin. Pin the other long edge of the hinge to the bottom edge of the back cushion. Hand sew the hinge fabric to the fabric on the cushions.
Pick up the deep seating cushion and slide it onto your patio furniture. Push it all the way back into the chair. You shouldn't be able to see the hinge between the seat and back cushions.