Using the Good Ol Plunger
The first step in taking care of a clogged drain is trying the age old method of using the plunger. Fill the sink partially with water, just less than a quarter of the way full. If you have a double sink, you will want to block the other drain with a cloth or towel. Plunge over the drain, up and down rapidly, until the water in the sink begins to drain. If it does, it was just a small obstruction and you should be ready to go.
Baking Soda and Vinegar
Empty the water from the sink. Add a cup of baking soda down the drain and pack it down.
Next, pour a cup of vinegar down the sink and put the stopper in immediately to force it down.
The mix will foam downwards into the pipes. Let it work for five minutes and then run warm water down the drain. If it is still clogged, try four cups of boiling water.
After this you can attempt to use something like a cable auger which is a lot more difficult or finally call a professional Plumber.