Pour boiling water down the drain. Then add a half cup of baking soda and let it sit for a minute. Pour a cup of vinegar and a cup of hot water down the drain. Cover loosely and let it sit for 10-15 minutes. Pour another pot of boiling water down the drain to flush out the clog.
here are some ideas from hometalk:
Remove as much as possible with a snake or drain cleaning tool. Pour ½ cup baking soda then ½ cup white vinegar in the drain and cover, letting sit for 20 minutes. Boil water, remove cover, and pour water down the drain. You may have to repeat the process.
It all depends on how the drain is assembled. My preferred method is to buy all plastic pipes etc and screw fittings. It's a doddle to take it apart and clean through with a toilet brush (not an old, used one).
However, if it's just plastic pipes all glued together, I like to push down a short length of wire used for hanging net curtains. With just a bit protruding, connect to a cordless drill and slowly ramp up the speed. Despite the twists and turns in the pipes, the spinning wire will begin to form 'waves' (like a sine wave). Nothing really survives in the pipe then. It also works a treat on the most stubborn blockages in toilets. Having worked maintenance in a residential care home, unblocking sinks and toilets was a major part of my work.
Pour some baking soda down the sink. Then pour some vinegar down. Immediately cover the drain with a cloth and hold down. The force of the foaming should push the clog through. If a double sink cover both drains. Follow up with hot water.