A friend recently gave me a small jar of asafoetida without telling me how to use it (or that it smelled horrible). In my googling, all I've been able to find out so far is that it's the dried sap of a Middle Eastern herb, used as a natural remedy, should be stored in a tightly sealed container due to its strong scent, and should be used "sparingly." I'm interested in knowing more specifically how I might use it in cooking (and if its flavor is better than its scent).
It is used extensively in Indian cooking. I have one book, Lord Krishna's Cuisine that calls for it in virtually every recipe, and each time reminds you to cut the amount down by 3/4's if you can't find Yellow Cobra brand. It does indeed have a flavor someone reminiscent of aged garlic. It is thought to have medicinal value as well (see the wikipedia article for details).
the Serious Eats blog had an article about asafoetida recently -- it also goes by the name "hing" (not sure if you ran across that in your googling).
the article is interesting (so are the comments), and offers some ways to use it:
Here's a whole website with recipes involving hing: http://www.manjulaskitchen.com/
It's very common in Ayurvedic cookery, which discourages/disallows onions and garlic and other alliums.
I am from the southern state of India, Kerala.
In our area (majorly in Southern India), asafoetida is generally used for making Sambar which is nothing but a curry with gravy and mix of different completely cooked vegetables. This is something which we have with Rice during Lunch\Dinner or with Idly\Dosa during Breakfast hours.
In addition to that it is being used in making Rasam, which is basically a soup like curry which is generally used with Rice during the last course during Lunch\Dinner or even drank as such. It helps in better digestion and keeps away different gastric problems.
I've never used it. I tried googling "asafoetida recipe" and found this page. http://health.learninginfo.org/herbs/asafoetida.htm It suggests sauteing a pinch in oil for an aroma similar to garlic or onion.