First, remove the basket strainer from the drain (see Fig. 1).
Run hot water until it stands about 2" deep in the sink (Fig. 1).
Take a suction cup plunger and pump up and down directly over the clogged drain. The water in the sink provides a seal. If the suction cup does not clear the drain in a few minutes, you will probably be forced to remove some of the pipes to get the job done.
If you cannot open the drain with the suction cup, set a pail underneath the sink trap (Fig. 2), and remove the cleanout plug and washer. If the drain is only slightly clogged, a few quick probes with a screwdriver may solve the problem.
If a few probes with a screwdriver do not open the drain, use a snake or drain auger through the pipe. A drain auger works best if you rotate it, feed it a short distance and then rotate it again. By repeating this, the drain auger can be inserted deeply into the pipe.
After the drain pipe is opened, replace the cleanout plug and washer and run hot scalding water through the pipe to carry away any accumulations.