Order a replacement armrest from the chair manufacturer. The manufacturer is typically listed on the underside of the chair or on a tag. If the chair is old, antique or you can not otherwise find the chair manufacturer, you can seek out a replacement piece at antique stores or resale stores. If this is the case, you may want to consider replacing the chair altogether. Additionally, a customized replacement armrest can be made by a professional woodworker, although this option can be quite costly.
Remove the bolts or screws that are attaching the armrest to the chair. A screwdriver, wrench or drill is best used for this step. Remove the old armrest after removing the attachments -- bolts or screws. Save the bolts or screws from this step in case you need them in Step 4.
Hold the new armrest up flush against the chair. Be sure that the holes the in armrest are lined up with the ones in the chair so that attaching will be easy.
Insert the attachment piece -- screw or bolt -- into one hole on the armchair and then into the armrest. Screw into place. Repeat for as many times as there are holes. Be sure to tighten so that the attachments fit snugly in place.