Cut is the most important determinant so you don't get a big, rare, but dull looking diamond.
These are the 3 areas to assess the Cut:
Proportion, Symmetry, and Polish
Proportion determines the path of light through the diamond.
Symmetry shows how evenly the diamond shines.
Polish decides how sharp the light is reflected off the surface of the diamond.
Diamonds are priced accordingly to weight categories, 1 carat=0.2 grams. The larger the stone, the more expensive, reflecting the rarity. Thus, diamonds of 3 carats and larger are significantly more prized.
Diamond colour grades typically range from colourless (Grade "D" being the rarest and most valuable) to light yellow or brown (Grade "Z"). Although most diamonds appear colourless, they actually have slight traces of yellow or brown caused by minute impurities within the stone.
Clarity refers to the degree which a diamond is free from naturally occurring inclusions. Clarity grading is done under 10x magnification and these inclusions are often called a diamond's birthmark.