Replace the sink trap to deal with buildup and clogged pipes that a plumber's snake or plunger can't fix. Replacing a sink trap is pretty quick work. You'll need groove-joint pliers, a bucket, and a replacement sink trap. (Take the old trap with you to the store to get an exact match.)
Warning: If there is any chance that chemical drain cleaner has been used to clear this trap in the past, you must take extra precaution when working on the trap. Wear rubber gloves and safety glasses to protect your skin and eyes in case of a water splash.
Put on your protective gear and place a bucket under the sink trap.
The bucket makes clean up much easier.
Remove the slip nuts.
Loosen the slip nuts with groove-joint pliers, unscrew the nuts by hand and slide them away from the connections.
Be sure to save the two washers that are part of the slip nut connection; you can reuse them with the new trap.
Pull off the trap.
The old trap will have some gunky water in it, so place the old trap in the bucket.
Slide the two washers from the old trap onto the new trap, and fit the new trap into place.
Make sure the washers have the wide side up so that is slides into the joint.
Secure the new trap.
Use the slip nuts to secure the new trap to the drain lines. Hand-tighten the nuts.
Run water in the sink and check for leaks.
If you see a leak, tighten the slip nuts one-quarter turn with groove-joint pliers.