The stopper mechanism in a bathroom sink works by shifting a lever to raise and lower the stopper. Although the stopper assembly has only a few moving parts, the stopper itself is generally made of plastic or vinyl with a metal cap at the drain plug. When the stopper stops working, it's generally a problem with the stopper stem wearing out, breaking or becoming clogged with soap residue.
Access the sink's drain line under the sink. The stopper mechanism can be seen behind the sink's vertical downpipe where the horizontal pivot arm attaches to the drain.
Detach the stopper's pivot arm retainer nut by turning counterclockwise until it is loose. Pull the pivot arm out of the drain pipe. You can use adjustable pliers to turn the retainer nut if it's too tight to loosen by hand. Allow the pivot arm to hang loose from the vertical stopper control rod.
Lift the old stopper upward out of the drain hole from above. You may have to extract the stopper by wedging the tip of a utility knife under the lip and raising it manually.
Insert the new stopper into the sink's drain hole, with the lower loop opening in the stem oriented toward the rear of the sink.
Reinstall the stopper's pivot arm into the hole in the rear side of the drain pipe, making certain the end penetrates the lower loop opening in the stopper stem. Secure the pivot arm into place by threading the retainer nut onto the drain pipe inlet and tighten until snug.
Test the smooth operation of the sink stopper by lifting upward on the stopper control rod behind the sink faucet's spout. Lift the control rod up to close the drain and push it down to open it.
Its a good idea to remove the old stopper stem and take it with you to the plumbing supply or home improvement store to match the replacement.