Most minor sink clogs can be cleared with a plunger. Partially fill the sink with water, then start plunging. Vigorously work the plunger up and down several times before quickly pulling it off the drain opening. If it's a double-bowl kitchen sink, stuff a wet rag into one drain opening while you plunge the other one. If it's a bath sink, stuff the rag into the overflow hole. In both cases, the rag helps deliver the pressure directly to the clog.
If plunging doesn't work, grab the cable auger and go to work under the sink. Remove the sink trap with a pipe wrench. The large, threaded coupling on PVC plastic traps can often be unscrewed by hand. Empty the water from the trap into a bucket, then make sure the trap isn't clogged.