Clear the sink drain of any solids or material, such as hair, that is stuck near the top of the drain using a pair of tweezers, then run warm water to see if the sink drains. If it does not, move on to the next step.
Fill the sink with approximately 3 inches of water, then place the plunger over the sink drain and work the plunger in an up and down motion several times, and quickly remove the plunger. If this method has worked, the water will drain immediately upon lifting the plunger. Repeat this step several times before attempting the next method listed.
Place a bucket underneath the S-drain pipe trap, which is shaped like an "S" and located under the sink. Remove the sink trap using the pipe wrench. Check the sink trap for clogs, and remove any debris you find.
Remove the horizontal trap arm that protrudes from the wall using your hand or a pipe wrench.
Insert the cable auger into the wall stub-out and feed it into the wall pipe until you encounter resistance. Once resistance is encountered, turn the cable crank clockwise and push it forward to break through any blockage. If the cable auger becomes stuck, turn the crank counterclockwise and pull it back, then resume pushing it forward once it is cleared. Continue on until all encountered blockage is removed.
Replace the horizontal trap arm and drain trap that you previously removed, then run warm water to see if the sink has been unclogged. If there is a slight backup of water, plunge the sink in the same manner as you did in Step 2.