Bathroom sink clogs are mostly caused by hair specially if a mirror is installed there and you brush your hair there.
Be sure the plunger's suction cup is large enough to cover the drain opening or your work will be an exercise in futility.
Fill the clogged basin with enough water to cover the plunger cup.
Coat the rim of the cup with petroleum jelly to seal the drain tightly.
Use wet rags to block any outlets - a sink overflow or second sink - and create a vacuum. By stopping up the overflow, you'll be sure to direct the pressure of your plunges down at the clog, and not out the overflow.
Use 15 to 20 strong strokes to plunge up and down once you have a tight seal.
If it doesn't clear, try this a few more times.
Don't use chemicals if the drain is completely clogged. These chemical will burn you skin; if they sit in a stagnant drain, you'll have to find a way to remove both the chemicals and the blockage. Don't use routinely because these cleaners can damage metal pipes.
Make sure the room is well ventilated.
Wear rubber gloves and eye protectors.
Read labels, and use the right kind of cleaner - an alkali to cut grease and an acid to dissolve hair, soap, and other gook.
Never mix chemicals, and do not use chemicals in combination with a plunger.
Don't look down the drain - chemicals give off toxic fumes and can boil up suddenly.
Drain auger is basically a long cable of coiled wire that will grab onto any clogs and allow you to remove them. Remove any filters or stops and guide the drain auger through the drain opening.
Work the drain auger patiently around bends in the piping as you feed it through.
When you've hooked the blockage, pull the drain auger back a little to free it, and then continue to push it through (or pull the clog out).
If feeding the drain auger through the drain doesn't work, try feeding it through a system cleanout.
Use a drain auger to snake a drain. For access, first remove the stopper, work the snake down the drain, and turn the handle to bore through the clog and push it through the pipe or pull it out.
For a deep clog, first remove the sink trap. To do this, unscrew the couplings (catch water in a bucket placed beneath the trap). Work a drain auger through the drain pipe to free or extract the clog.
For sinks there are various ways by which you can prevent clogging.
Use a screen over your sink, you can buy drain screens in any hardware store or home center. You simply position these over the drain, and they catch any hair or lint--before it goes down the drain. Simply clean the screen out regularly, which is much easier than snaking the drain!
Once a month, clean the drain with a mixture of baking soda and vinegar. Simply shake some baking soda down the drain, then follow with a bit of vinegar. There's no measuring needed here--once the baking soda/vinegar mix starts foaming up, you know you've got enough vinegar. Let this work for about five minutes, then follow with boiling water. This will keep your drains clean, as well as deodorized.
Bathroom clogs can be annoying, but they don't have to be a catastrophe. And, now that you know what to do, they don't need to be costly, either.