Cleaning the P-trap
Place the bucket under the P-trap to catch any water that drips out.
Loosen the compression nuts at both ends of the P-trap. If the pipes are metal, use the slip-joint pliers or adjustable wrench to loosen the nuts. Wrap a rag around the nuts to prevent scratches. If the plumbing is PVC, no tools are used. Loosen the nuts by hand.
Separate the P-trap from the drain pipes. Water will be in the trap so be sure the bucket is positioned to catch it. When the P-trap is free from the other pipes, turn it over and empty the remaining water into the bucket.
Clean out the clog in the P-trap. Rinse out the P-trap in another sink or outside to clean all of the soap scum from the walls of the pipe. Leaving it in place will trap more debris sooner.
Reassemble the P-trap to the fixed drain pipes. Be sure that any compression washers are seated before the nuts are retightened. PVC nuts should be tightened by hand only. Metal nuts can be tightened with the slip-joint pliers or wrench, but be careful not to over-tighten them and destroying the threads.
Run water down the drain to test for leaks. Keep the bucket in place in the event that a leak should appear.