For a clogged drain you will want to first attempt to use a plunger. Fill the sink partially with water. If it’s a double kitchen sink be sure to plug one of the drain openings with a rag. If it’s a bathroom sink plug the overflow hole with a rag. This ensures that the pressure from plunging is directly delivered to the clog. Work the plunger strongly several times and then quickly move the plunger from the drain opening. This may need to be attempted several times. If the sink doesn’t drain you will need to use a cable auger or plumbers snake.
Cable augers are available are available up to 100ft lengths, but for home use 25ft should suffice. Under the sink, remove the P- trap with a pipe wrench. Empty the water from the P- trap and inspect to be sure the trap itself isn’t clogged. Next remove the horizontal arm that protrudes from the wall. Insert the cable of the auger until you feel resistance. Pull out approximately 12-18 inches of cable and then tighten the lock screw. Turn the handle in a clockwise direction while pushing forward. This pushes the cable farther into the pipe. Pull another 12-18 inches of cable and repeat the above process until you break through the clog. If at any time the cable catches or becomes bogged down, turn the crank counter clockwise and pull back. Once the cable is clear, resume pushing forward.
Once the blockage is cleared, replace the P-Trap and arm. Run hot water to ensure proper drainage. Debris from a broken clog may not drain quickly. If your sink drains slowly use the plunger method as stated above to clear the debris. Flush with hot water after.