So, you have turned the water on in your sink to wash your hands or shave. You finish your business and the water is not draining out of the sink. You toggle the plug several times to see if the results are different, but they are not. You have a clogged up drain, and here are some ideas and remedies to try.
The first thing to try is to pull the sink stopper out and see if that undoes the clog or jam. You will have to twist it back and forth to jimmy it out. If it does come out, the sink will probably drain and you will witness an awful collection of hair and slime on the sink stopper. You need to clean this up, and while you are at it, reach into the drain hole and pull out any offending gunk. At this point, with any luck, the clog is gone. Run the sink to confirm.
If this does not work, the next thing to try is to attack with a plunger. These can be used for sinks as well as toilet bowls. Get a good seal over the drain hole and pump it hard, up and down, 6 or 7 times. This typically solves the problem. If it does not, try it again, and if necessary a 3rd time.
If the problem still persists you can consider any number of over the counter liquid drain cleaners that my cut through the blockage. The challenge with these is that they are highly toxic and dangerous chemicals, which while they clear the blockage from the pipe, are also bad for the pipes and bad for our environment. They are also very dangerous if somehow by ingested by homeowners. They can be effective if they do not cause other damage.
If after all of this the clog still persists, then it is time to call in your professional plumber and they will the tools to unclog the drain.