Lift the chair and place it on a worktable so you can easily access the damaged spindle. Grasp and wiggle it out of the socket or holes so it comes loose. Pull the back or leg of the chair holding the spindle in the opposite direction so it comes out easier. Alternatively, remove the screws that attach the spindle to the chair with a screwdriver, or drill a small hole through the base of the chair that meets the spindle, if no hole already exists. Using a hammer, tap a center punch into the hole to loosen and release the spindle.
Insert the tip of a pointed knife or long nail into the spindle holes in the chair to remove accumulated wood adhesive, dirt and grime. Tap the knife or nail with a hammer to loosen stuck sections of adhesive. Wipe the chair surface with a damp cloth.
Inspect the spindle to determine the extent of the damage. Spread wood glue over the broken section of the spindle or insert it into a crack with a putty knife. Use a vice to hold the glued sections together for the time specified on the label directions.
Apply a bead of wood glue into the holes in the chair where you will replace the spindle. Also, apply a small amount of glue to each corner of the repaired spindle.
Position the repaired spindle into the glued holes in the chair. If required, pull the back or leg of the chair away so you can easily insert the spindle into the holes. Replace any screws you removed.