Cognac and Brandy are made from wine which has been distilled into a liquor and aged, usually in wood and often for decades. Therefore they are a product of both fermentation and distillation.
Cognac and Brandy are the same product, but in order to be called "Cognac", the liquor must come from the Cognac Region of France. It must also be made according to the strict standards of that region. The common French term for the wines which go into cognac is eaux-de-vie (literally, "waters of life") and refers to a double-distilled wine. All cognac is brandy...but not all brandy is cognac.
Cognac and Brandy are typically served neat, in a snifter or tulip. You may warm the glass, however this tends to cause the alcohol to vaporize and can ruin the nose of a truly fine cognac. If you are not in a tasting scenario where this is crucial, warming the glass is often viewed as a classy and sophisticated thing to do.
Cognac and Brandy are occasionally mixed in cocktails. This can be good. Sadly, some people mix them with Coke. This is bad. That being said, remember it is your job to give your guests what they want, whether it's bad or not.
Cognac has a star-rating which is strictly enforced by French law.
The official quality grades of cognac are:
VS Very Special, or *** (three stars) where the youngest
brandy is stored at least two years in cask.
VSOP Very Superior Old Pale, where the youngest brandy
is stored at least four years in cask, but the average
wood age is much older.
XO Extra Old, where the youngest brandy is stored
at least six, but average upwards of 20 years.
There are other grades, such as Napoleon, which is
roughly equal to XO in terms of minimum age...meaning
it must be at least 6 years old. Don't expect this to be the
same quality as a bottle labeled XO, though...there's a big
difference between 6 and 20, and most producers using
the XO label are on the high end of the scale.