Unzip and remove the old covers from the cushions. As you go along, keep track of which old cover goes with which cushion and with which new pieces. This will ensure your new covers fit their corresponding cushions properly.
Remove the seams of each old cover carefully with a seam ripper. Lay the new fabric out face-down on a flat surface and lay the old pieces face-down on top of it. Trace around the pieces with a fabric pen and cut out the new pieces with scissors; keep all of the corresponding pieces together.
Pin the pieces of the first cover together using the old cover as a guide. Make sure that you pin the pieces with the wrong side of the fabric facing out. Sew the pieces together, removing pins as you go, but leave the top seam open.
Pin the new zipper upside-down along the top edge that you left open. Sew the zipper into place, making sure that nothing blocks its path. Turn the cushion right-side out; reach into the cushion and poke all of the cushion corners out fully with your index finger.
Zip and unzip the cushion cover to text that everything works properly. Construct the rest of your cushion covers and insert each cushion into its correct cover, zipping them closed.