After checking the solidity of the structure and the joints of the various parts that compose it, check the coloring of the chair.
If necessary you can repaint or wax and pat the structure to give a more "antique" look to the wood.
But let's see the two techniques we can use in this case.
After passing the entire surface with thin sandpaper or steel wool, pass the surface with alcohol to degrease and highlight the wood grain.
You can darken the color of the wood at this stage by applying some stain and then going over the surface with sandpaper to remove the fibers raised by the stain.
To obtain the waxed effect at this point, apply the shellac with the cotton swab in two or three coats. At this point rub with a cotton cloth.
After applying the entire surface with thin sandpaper or steel wool, apply the base and one or more colored coats.
Apply a coat of "glacis" paint to this effect to coat and give the antique effect, you can buy it ready-made or make it yourself by mixing the base paint, the water-based paint for the wood and 2/3 teaspoons of natural coloring earths.
After this step, pass the piece of colorless wax or water-based varnish onto the piece.