Do not cut your webbing at this stage; if you inspect it you will see that one side has a rough surface and this is designed to be the top in use. (The idea is that it prevents the cushion slipping on the webbing but if you find you have put it on upside down it won’t make much difference so I shouldn’t worry).
Make sure the end of the webbing is cut straight at 90 degrees. Insert the end of the webbing into the metal clip with the metal lip on the back of the webbing. (The webbing folds over the metal lip and it stops it rubbing on the frame.)
Insert the clip into a vice leaving the lip resting on the top of the vices jaws and tighten the vice which compresses the clip without damaging the top lip. Inspect the tightened clip to make sure the webbing is completely into the clip and the metal teeth can be seen to have pierced the webbing.
If you do not have a vice you can complete this stage by cutting a shallow groove in an old piece of wood and resting the lip of the clip in the groove. With the webbing in place tap the top of the clip with a hammer to close it. Inspect the tightened clip to make sure the webbing is completely into the clip and the metal teeth can be seen to have pierced the webbing.
Once you have a clip on one end of the webbing insert it into the chair frame and lay the webbing across the seat and whilst holding it under tension mark where the webbing crosses the top of the groove on the other side of the chair. Cut the webbing at this point and fix a second clip onto the other end of the web. The distance to the bottom of the groove should ensure the correct tension on the finished web which should have no slack but not be obviously straining so that the web narrows.
Once you have the first web the correct length you can use it to mark the correct length of the others.
You also can buy ready made straps.
The type of clips on a photo (click to enlarge) is no longer available to the best of our knowledge.
If you have such clips, you can buy webbing by the m and re-use old clips by carefully opening them up with a screwdriver, that would be best.
Otherwise, the new clips can be used with a self-tapping screw inserted into the slot to hold the clip in place. Your straps need to be ~1” or a bit more longer in this case.