Remove drain plug and any gunk & hair that is in the path and you can get out. There's a cheap plastic tool you can run down to grab that kind of material.
1 cup baking soda
1 cup white vinegar
cover and let the chemical reaction happen
Boil water and pour down the drain
This should take care of anything short of a severe block.
vinegar and baking soda
For future avoidances - try the TubShroom and SinkShroom. Sold on Amazon. Really works well for preventing clogs!
most bathroom sinks are not clogged with food / grease and the vinegar/soda will only help --- they usually suffer from a 'HAIRBALL' ... Amazon, and most home improvement stores carry what they call 'HAIRSNARES' for hair removal from bathroom drains ...