If your sink is clogged, you should first assess whether or not it is regular buildup or a foreign object. Kids often shove their toys where they don't belong, but other items, such as caps and lids, can make their way down the drain as well. Those things aren't made to make it past the pipes, so they will get stuck and may back up the water that tries to go down. If that is the case, these home remedies will not work. You may need to use a tool to pull the object out, take apart the drain or call a plumber. The last may also be necessary if the clog is very bad.
If regular use seems to be the problem, however, these remedies can be easy and effective. They may also save you from having to purchase a caustic, chemical unclogging agent.
The first option you have is also the easiest: boiling water. This is especially effective for grease buildup. Fats can solidify in the pipes, so very hot water can help melt the grease and make it move along. If you have a kettle or tea pot, use that to bring water to a boil; it is easier to maneuver when you pour it down the drain, but a regular pan will work as well. Use caution so you do not burn yourself or splash boiling water on yourself. Slowly pour the hot water into the sink. If there is no standing water, direct the water directly into the drain. Do not use this if your pipes are plastic, however; try hot but not boiling water instead.
Another remedy that can help unstop a sink is baking soda. Dump about a cup of baking soda into the drain, and follow up with approximately three cups of hot water. The baking soda, when combined with the hot water, will become slippery. This will hopefully help loosen and break up the plug, and encourage the plugged contents to move down the pipes.
Baking soda is part of another remedy, too. If baking soda and hot water alone did not help unstop your sink, put about ½ cup of baking soda in the drain, and follow up by slowly pouring in ½ to 1 cup of vinegar; white vinegar or apple cider vinegar are both fine for this use. The two will react, creating a foaming action that can help break up the clog. Allow the combination to work for an hour or two, then flush the drain with hot or boiling water again.
If you have a small plunger, you can try using that directly over the drain to help pull out the plug. You will need to have water in the sink while plunging, so if there is not already standing water in the sink, run water until there are two or three inches in the sink.