If your cushion is in good shape, use it as a pattern for you fabric. For my chair it was best to get a new piece of foam. It's very expensive, but I was lucky enough to tackle this right in the middle of JoAnn's 50% off sale on high density foam. This is a yard of 4" foam. I traced the old cushion and cut out the shape with a serrated bread knife. If you have an electric carving knife, that would give you a smoother cut. By the way, this stuff smells terrible at first but I don't notice a smell anymore.
Pin the welting onto the fabric following the edge of the foam. Pin the corners and cut some easing snips into the curves to imitate the fit you want. I didn't have enough matching fabric to cover the whole cushion, so I bought some black duck canvas to use on the parts that don't show. In the picture above you are looking at the bottom of the cushion.
Hide the spot where the welting ends overlap by snipping open the seam of one end and trimming back the cord inside until it is long enough to just reach the other welting end. I did this to the piece on the right side, then inserted the left end of welting and sewed them closed together.
The finished bottom of the cushion! Sew the welting on, and then do the same to the other piece of fabric.
When both the top and bottom pieces are prepared, lay the top piece on the foam, right-side down, and pin the edge pieces to it, also right-side in. I have a seam in the side fabric in the picture above because I was down to remnants, but you should cut out one long strip to cover the front and reach a little more than halfway up the sides.
I checked the fit by turning the pinned material right side out and placing it on the foam. The pins distort the edges a bit, but it's beginning to take shape! I sewed the pieces together along the pinned lines, always feeling under the fabric to make sure I was staying right next to the welting. Attach the front half of the bottom piece in the same way.
For the back half of the cushion, I followed the same process but used two pieces of fabric, long enough to overlap each other. This leaves room for inserting and removing the foam. I also used spray adhesive to attach a layer of batting to the top and bottom of the foam inside.
Because it overlaps, I can add velcro to hold it closed. Whichever one ends up looser goes on top.
Here's the finished cushion! And now, please excuse me while I pump my hands in the air and dance around to celebrate the end of a very long project.