Use a drain auger by extending the cable, feeding it into the drain, tightening the setscrew and turning the drum to remove the clog. If working on a clog in a toilet, use a toilet auger, which has a special tube to direct the flexible cable into the drain without scratching the porcelain.
Most sink augers are in an enclosed drum that provides the leverage for turning the cable to clear the clog. The drum also provides storage for the cable. Loosen the setscrew, and pull the cable to extend it so it is long enough to reach through the trap. Turn the screw to tighten the cable. Remove the stopper from the sink, and push the end of the auger into the opening. Continue pushing the cable forward until reaching the clog.
Place one hand loosely around the conical tip of the auger, and use the other hand to turn the drum and cable. Continue turning and feeding more cable until the sink starts to drain.
If enough cable is extended to reach through the trap but the sink is still clogged, remove the auger from the sink. Place a bucket under the trap to catch any water inside, and remove the trap. Insert the auger into the portion of the drain that enters the wall, and continue working to remove the clog.