If the clog isn't too severe sometimes boiling hot water can clear a clogged drain.
It's best to remove the standing water from your drain using a shop vac and then power a cup of baking soda down the drain and then pour 2 cups of vinegar down the drain and cover the drain up and leave it for around 30 minutes to 1 hour.
Baking soda and vinegar will usually clear clogs out of drains including dissolving hair in the drain.
If that doesn't work you may need to remove the P Trap below the sink and see if a clock is in there.
Drano is also another great chemical for clearing clogged drains although it takes awhile to work but when it does work it does work although you need to ventilate your home when using the Drano.