If you are having trouble with just one sink draining, then more than likely you have a stoppage in the immediate drain line. These can usually be removed by using a drain snake to clear the line. However, if it is further down the line you might not be able to reach it with a regular drain snake, and you should call your plumber. If the water is draining slowly then you might have what is referred to as a partial stoppage which is allowing some water to pass through at a much slower speed. The first thing you should check is the pop-up to make sure there aren't any obstructions like hair in the line. If there are no obstructions that you can see, you can try using a drain cleaner to remove the debris in the line.