A slow-draining kitchen sink is likely caused by food or grease accumulating inside the pipes. If you have a double sink and just one side is running slowly, the clog may be in the trap--the u-shaped pipe that leads from each sink. However, if both sides are slow-draining, the problem is further along in the system. You can fix a slow-draining sink in three ways.
If the clog is in the elbow, try dislodging it with baking soda, vinegar, and hot water. Begin by packing the drain with baking soda. Pour vinegar slowly on top. When the mixture stops fizzing, pour a pot of boiling water into the drain. The sink should immediately unclog. If it does, run hot water for a few minutes to ensure that the debris is completely removed from the system. This approach works for a combination of reasons. The fizzing action moves the food particles, and any excess vinegar acts as a natural solvent because of its acetic acid. Tthe water pushes along the clog while its temperature melts any grease. If this doesn't work, try a commercial solvent.
If baking soda and vinegar don't work, try a drain-cleaning product. Bacteria-based products are favored by environmentalists. These bacteria-based products send colonies of bacteria into the drain which then feed on the clog. This approach may take repeated applications. After pouring the cleaner into the drain, the sink should not be used immediately. Pour the cleaner in before bedtime to allow time the colonies time to work without water washing them away.
If neither of these approaches is successful, the clog is likely far down the line. In this case, an electric rooter will ream out the food and grease creating the clog. Generally, a hand twist rooter, or snake, will temporarily fix a slow-draining sink by punching a hole in the blockage. This hole, however, may soon clog up again. An electric rooter, either rented from a u-rent shop or wielded by a professional plumber, uses a bulb or hook to clean the pipes thoroughly.