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Place a bucket under the p-trap, and put on rubber gloves.
Use a pair of slip-joint pliers to loosen the nuts on the trap, then slowly remove the trap and dump out the debris and water into the bucket. If the trap is at all damaged or rough inside, replace it.
Once the trap and trap arm are removed, pull out about 18" of the snake -- also known as a hand auger -- and tighten the lock.
Work it down the stub out in the wall until it's all in the wall or you feel the clog and can break it up.
Continue this process until you pass the clog. If the cable gets snagged, just turn the crank to work it through.
Remove the snake and replace the trap.
Run water down the drain to see if the clog is cleared.