If your bathroom sink is slow to drain you may need to unclog the U shaped drain under your sink called a pea trap as well as remove the plunger to clean out the drain. The tools you will need are a small bucket and a large sized bucket as well as an old toothbrush. You should remove everything from under your sink to ensure you have enough room to work.
The first thing you will need to do is to place the small bucket under the pea trap to catch any water that may still be in the drain. You will want to remove the pea trap that is the U shaped pipe under the sink. There will be two nuts that you should be able to unscrew by hand unless there is a lot of buildup on the nuts. It there is build up you will also need an adjustable wrench. Loosen the nuts and slowly remove the pea trap from the drain. Be careful because any water remaining in the drain will start dripping into the bucket. Clear away any visible debris from the drain. Then take the pea trap to a different sink and clear out any remaining debris. Then scrub the pea trap with the old toothbrush and rinse it out well.
Now remove the plunger from the sink by unscrewing the rod attachment from the back of the drain under the sink. Pull the rod out of the attachment. The plunger should be able to be removed from the sink basin now. Look down through the drain even if you can see all the way through the drain may still have hair and other particles in it. With the large bucket under the drain run a small stream of water and gently scrub the drain with a tooth brush. Do this at the basin entrance and from the bottom of the drain. Put the plunger back into the basin carefully aligning the notched opening to the back of the sink. Then insert the rod back through the opening in the drain and then tighten the nut. Place the cleaned pea trap back onto the drain and tighten the nuts.