You can unclog a sink with standing water by removing the standing water first using cups or a wet dry vac to suck out the water in the sink.
Then take a 1/2 cup of table salt and pour the table salt down the drain and then pour some boiling hot water down the drain after you put the table salt into the drain.
Let it sit for a 5 or 10 minutes and then flush the drain out again with hot water.
If it's still clogged you may have to remove the P Trap below the sink to clean the clog out or snake the drain line to clear out the clog if it's further down the line.