You can take off the old upholstery and staple on the new one. See more details here: https://www.aratariathome.com/blog/dining-room-chairs
It depends on the chair style. Do you have a photo
This Delois, relies on if you already have upholstered chairs or if those are Bare without upholstery atall.
I always recommend: Supergluing Zippers on Fabric so you can Clean them in the Washing Machine, because it is easier than dealing with Velcro.
This much less fails than those Tie on Stringy-Ding Ripoffs (that you always gotta replace after 1 Obese Person adjusts their Behind on the Cushion rather than Standing Up to Fix their Underpants).
Basically all you do to make a Cushion is Make a 1/4 Cube out of Fabric and Stuff it to the Gills.
My Perspective on Needle and Thread is: if Surgeons stitch up faces with Superglue, you better believe Superglue is even better on Cushions for my ass than Stitches.
Delois...there are usually screws in the bottom that you can remove. You may be able to use the old cover as a pattern for the new as well as the foam that may be reused or replaced. It's really not hard, pull tight and use a staple gun. You may want to cover the bottom with fabric or a liner of some type just so it will look finished.