I picked up this recipe from Reader’s Digest (More Extraordinary Uses) some time ago and have tried it and it works.

One cup baking soda
One cup salt
Quarter cup cream of tartar
One cup boiling water
Put the baking soda, salt and cream of tartar into a glass jar and shake vigoroursly.
Pour a quarter cup of the mixture down the drain.
Follow it up with a cup of boiling water.
When the fizzing stops, flush with cold water for a few minutes.
If you are without these ingredients but have a tennis ball, cut it in half.
Put the hollow part over the drain outlet and press down firmly several times with one hand on top of the other.
The suction should clear the drain, at least temporarily.