Although Fernet is not originally an Argentinian liquor, it is widely popular there. It's probably due to the large influx of Italian's in Argentina during the 80's that to this day, it is the most popular alcoholic drink in this country.
Fernet is a bitter, made with a variety of herbs and spices, and it is often served as a digestive after food, and also mixed with coffee. There are many bands and flavors, but the most popular in Argentina is Fernet-Branca. Interestingly enough fernet was allowed during prohibition times in America since it was considered a bitter and not an alcohol.
How to drink Fernet?
Fernet is often served mixed with Coca-cola. The sweetness of Coca-cola balances well the bitterness of Fernet. Fernet has a very strong, herby distinct taste and you will either love it or hate it. A lot of people say that Fernet reminds them of medicine, which it kind of is.
If you are in the States, especially in the Bay Area you will see people drinking Fernet as a shot and chasing it with ginger ale. In fact, one of our friends introduced us to a mint flavored Fernet in San Fransico and we have been drinking it ever since.