To appreciate an excellent armagnac, one must consider the...

Visual   aspect

Its limpidity : brillant, clear, dull
Color intensity : light, medium dark
Its smoothness along the side of the glass

Olfactory aspect

One has to be patient and not plunge its nose in the glass to avoid beeing immediately saturated by the fragances.
You should try to appreciate the intensity of the aromas, agressivity, fineness...
You should also try to grasp the vanilla aromas, the violette, prune and wet leather perfumes :
The olfactory pleasures are unlimited.

Gustative impressions

It is expected to appreciate the sweetness, acidity, magnitude, sharpness, dryness, bitterness, roundness, the aromatic persistence, etc.
A good quality armagnac shows an important roudness and aromatic persistence.
A dry quality armagnac or which has an important bitterness, can not be called a product of quality.