I was lucky enough to find a couple of mid century modern dining chairs on ebay, but the covers were dull as ditchwater and needed replacing. I found a great upholstery fabric at https://www.craftysewer.com/ that gives more than a nod to mid century. I loved the colours on the underside of the fabric so I have used it reverse side up.
You will need
Unscrew the seat from the frame.
Place seat on fabric, and cut out the fabric including a 4in overlap.
Staple on the fabric at each of the 4 corners, as shown in the picture.
Fold and turn the edge fabric over each side of the chair and staple into position. Screw the newly covered seat back onto the chair.