The demo chair I found at a thrift for $12.00 and the previous owner had used jute webbing nailed to the frame. I'm sure it served it's purpose until they decided to get rid of the chair and I came along to purchase and set new 2"elastic webbing and v-clips, as the manufacturers had intended. I took some artistic license (and economic practicality) with the height of the seat, using a 4" leftover foam I had in shop, instead of a flat cotton pad or up to 3" foam that would be standard for vintage Danish - still it sits wonderfully with new webbing underneath.
Flattening the v-clip can happen a number of ways - pliers, vise, boot heel. I do like to give it a few whacks with a hammer against table edge in order to make the teeth set into webbing though -
Work from back slot stretching the length taut, but not too tight to the front and make a mark with chalk where you should cut at the slot. Flatten a v-clip to this new strip of webbing and place it in, woo-la!
Keep going until you have all the verticals done, then do the horizontals by weaving them in and out. Not all chairs will have both directions - many frames just use vertical webs, but you get the idea. Don't worry - it'll be great - you really can't mess up, unless you pound the v-clips too flat and they slip out because you cut a strip too short by pulling too tight -- so don't do that!