A quality grade estimate is performed by a Federal Grader as part of the USDA's Agricultural Marketing Service. A Grader assesses the Quality and Yield grade of a full or half carcass. The Quality grade is the USDA designation that can be found on most meat you buy - Prime, Choice, Select, etc - and is primarily determined by the maturity (age) and degree of marbling. The Yield grade is essentially how much lean is in the carcass, it is an estimate of how much sellable retail product there is available, and how much fat and bone is going to need to be thrown away. The wholesaler is pretty much the only person that looks at the Yield grade.
Just about the entire Quality and Yield grade is done by looking at the cross-section (the ribeye) between the 12th and 13th ribs. All this is done in the span of 10-12 seconds per full or half carcass.
Maturity is determined by looking at the color of the meat and the chine buttons. As the animal gets older, the meat goes from a cherry red to a darker red color. The chine buttons are the white, soft, cartilage tissue right along the end of the backbone. As the animal get older, the cartilage hardens into bone in a process known as ossification.
Marbling is determined by the flecks of fat that are evident on that exposed ribeye.
The yield grade is then determined by the thickness of fat surrounding the ribeye, and comparing that to how the fat looks around the Chuck, Brisket, and Round.