There are 4 factors that determine the price of the diamond: Color, Carat, Cut and Clarity.
Diamonds are usually colorless but they can go from no color to a lightlu tinted yellow. Most people look for a colorless diamond, but they are also the most expensive.
Colored diamonds are very rare and therefore very pricey. Pink is the most expensive of them, as it is the most rare one, with Blue being second most expensive, starting at about $30,000 per carat and going up to $200,000.
Speaking of carat, they are not all alike. Price of the carat varies and depends on the clarity of the diamond and the quality of the cut . A Carat weights 200 milligrams, 1/5 of a gram, so the carat rating is based on the stone weight, not size.
Cut of the stone also affects the price. Round cut diamonds are the most popular and most expensive ones. Asscher and Cushion cut diamonds follow closely. Here you can find more information on diamond engagement rings cuts.
Clarity is a quality of diamonds that is related to the existence and visibility of internal characteristics of a diamond, inclusions, and surface defects called blemishes. Inclusions can be either foreign materials in the diamond or structural imperfections such as tiny cracks. The size, color, number, location and visibility of inclusions all affect the relative clarity of a diamond. Clarity grade is based on the general appearance of the stone under 10x magnification.