The easiest, safest method for unclogging a sink drain is to use a plunger. For dual-basin sinks, plug up the unclogged drain, and add enough water to the clogged basin to cover the top of the plunger. Then work the plunger straight up and down over the drain to force the water through.
To help prevent future clogs, pour 1/2 cup baking soda into each drain, followed by 1/2 cup warm vinegar. The reaction between the acidic vinegar and the alkaline baking soda will loosen any debris in the drain, and the baking soda will help keep the drain smelling fresh.