Okay, I have 7 pics, with comments. Your seat frame has 3 tiers 1) the top surface, 2) the first tier is for your fabric and padding, and 3) for your seat support and padding, also.
I'd recommend you get some jute webbing for your seat support. A whole 72 yard roll will cost about $40 on Amazon - https://www.amazon.com/Mastex-Jute-Webb ... WV6W1NE2HW
Your local fabric store should have jute webbing. You will weave your webbing over the seat frame - https://www.flickr.com/photos/43836144@ ... ed-public/
Extend the length of the webbing about 3/4" beyond the perimeter of its tier. Staple or tack it down.... 4 or 5 staples or tacks - https://www.flickr.com/photos/43836144@ ... ed-public/
Fold back the extended end and staple it again 4 or 5 times - https://www.flickr.com/photos/43836144@ ... ed-public/
Next, lay some heavy cloth (like denim) or burlap over the webbing and attach along the tier edges. Pic shows synthetic burlap, but any heavy strong cloth type material will do. Also, my pic of burlap only covers part of the edge. Your burlap needs to extend to all edges. Attach top and bottom centers to align it, pull it snug and staple/tack it about every 2 " all along the edges - https://www.flickr.com/photos/43836144@ ... ed-public/
Next is your padding. Pic shows cotton padding. any good seat padding is fine, just make sure it's not too thick. Attach the padding every so often along the very inside edge of the next fabric tier. Don't attach your padding too close to the upper surface of the seat.... attach it closer to the webbing/burlap edge. Do you understand this? If not, I'll take another pic or two. You don't want the padding right where you will attach your fabric. That fabric tier is to share space for your padding and for your fabric, so divide that tier for attaching each. Understand? My pic doesn't show the actual attachment. https://www.flickr.com/photos/43836144@ ... ed-public/
You want to attach your fabric right up against the edge of its tier. You might want your fabric to extend over the edges, a bit, then cut off (razor blade/knife) any excess after you finish installing the fabric. Attach the top and bottom centers of the fabric first, aligning your fabric if it has a pattern or if you are centering a print or design. Don't stretch your fabric, but you do want it fitting snug across the span. After the first top and bottom center attachments, make one attachment each side of the top, then one attachment each side the bottom. Repeat this process as you work across the seat, then attach your sides similarly. When snugging your fabric across, make sure you apply tension not only front to back, but also side to side.... apply all of this tension evenly. It takes a little practice to get the hang of it, so that your fabric/pattern (if applicable) stays straight, firm tension, feels right, etc. In a way, the type of padding sometimes dictates the tension/tensions to be applied. Use your judgement as to what may be a good fabric tension for your particular seats. https://www.flickr.com/photos/43836144@ ... ed-public/
Once your seat is done, you may want to apply a dust cover on the bottom side of the seat. Usually a black cover is used. Install it fairly snug across the span. Probably most of your upholstered furniture has dust covers on them. Look at them to see what it is and how installed.https://www.flickr.com/photos/43836144@ ... ed-public/
For the edges of your finished fabric install, you can install nails. *I haven't reread your previous posts... did you want to reinstall leather, or will you install cloth fabric? If you install cloth fabric, then gimp might be best for your chairs. The nail holes in your chairs looks like nails may have been installed initially, spaced about 1.5" apart. That was fine for what I suspect was your previous oil cloth or leather.
A note about leather: leather is sold by the hide or half hide, not by the yard as cloth fabric is sold. Calculate your needs as per fabric yardage or by leather square footage. Hides are measured and sold by square foot. Not all leather outlets sell half hides, only some do.
Probably some of the pics and/or explanations are vague. Ask for more info if need be. Your local fabric shoppe should have all supplies needed, except for leather, maybe.