Fit the plunger over the sink drain while wearing work gloves. If you have a double sink, insert the stopper into the other drain.
Push the plunger handle up and down to create a suction that may dislodge the clog and allow the backed up water to drain normally.
Remove the plunger and guide the pointed tip of a drain snake down the sink until you feel resistance. Crank the handle on the drain snake to rotate the auger on the end, inside the pipe. Keep cranking until the handle turns easily, which is a sign you have pushed through the clog, and then back the auger out.
Run hot water from the faucet down the drain to clear the pipe, unless it remains clogged.
Pour the recommended amount of drain cleaner directly into the sink hole based on the instructions printed on your drain cleaning product. When the required wait time has passed, run hot water down the drain to clear the clog. In the rare event that the pipe still won't clear, the clog may be deeper in your plumbing than can be reached with consumer tools. Contact a plumber for repairs.