Turn the chair over and inspect the caster to determine the type of caster. Stem casters have a rod that slides into a hole; some screw in and others just rest in the hole. Ferrule casters slide into the base of the furniture leg and screw into a metal socket. Plate caters have a flat plate that mounts on the bottom of the chair.
Remove the caster from the bottom of the chair by slipping it out of the hole or unscrewing the caster or plate from the bottom of the chair leg. Use a screwdriver to loosen and remove screws on plate casters. Bring the caster with your to the store to match it with an exact replacement.
Insert the new caster into the hole on the bottom of the chair. If you have a screw-type caster, insert the caster into the hole or metal socket and turn clockwise to tighten. If you have a plate caster, line up the plate to the bottom of the chair leg and sink the screws in with a power screwdriver.