They’re an easy one.
Unscrew the seat pan from the bottom.
Staple the new fabric to the bottom & re-attach.
Spend a dollar more per chair on suitable upholstery fabric.
Cotton, rayon & acetate are not suitable.
Some polyester “pills” but not all. Nylon is good.
Acrylic can stain with hot food spills, like coffee.
But olefin and polyolefin are the worst at oily foods stains.
There are some really fun vinyls our there.
You can have them upholstered or cover with material and color of you choice. With seat covers that slide on.
If you need help understanding how to remove the old fabric, check out my post.... https://karupp-did.net/fabric-removal/.
In this post, I show you how to remove old fabric from a bench. Bench, chairs, it is all so similar in removing the material. You will use the old material as a pattern and cut the new fabric according to the same size.
Then check out my post https://karupp-did.net/bench-part-3/
In this post I show you tips and tricks how to staple it all back together. This project was a bench but it will really help you see how to staple to make a nice tight fit.
If there are any curves in your dining seat, check out my post https://karupp-did.net/re-upholster-with-white/
This post I go into detail how to re-upholster a seat with a curve with thick fabric. if your seat fabric is thinner upholstery and are going to get a ton of traffic you might want to spray with a scotch guard spray. You might need a couple of coats. Anyway, hope these ideas helped. Good luck!
After using a cotton plaid fabric that went well with my then d.r. wall paper, I replaced the upholstery with white fake leather. It is an easy job. It is important how you staple the new covers though, start in the middle of one side, move across the seat to the middle of the opposing side, then do the middle of one of the remaining, middle of other remaining side. Do this, not really staple by staple but alternate often. That will keep fabric smooth and "squared" This is a very satisfying job.