Since there are so few breeds of geese available, determinining what type of goose you have is extremely simple. Also, since these breeds come in few, if only one, color, discovering that what you have doesn't match anything on this list virtually gurantees it is a mix. Breed identification is broken down into four parts: the head, color, feather type, and size.
This list only shows the recognized breeds available in America that are also recognized by the APA (American Poultry Association). Some geese, like the critically rare Cotton Patch, or the Lavender Ice and American Blue developed by Holderread, are not included since they are unlikely to be what you have, being exceptionally hard to come by.
Also, as with all things, remember that mixed geese can be as useful to you as purebreds. While purebred geese need the support of breeders to keep their numbers strong, above all else people need to find joy in having geese, no matter what they are. As more people are reintroduced to the benefits of having a small flock of geese in the backyard the number of individuals who dedicate themselves to helping a critically rare breed will also increase.
Head
Bill: Most geese have a normal bill that blends smoothly from the forehead and tapers into a triangle. There shouldn't be any bump or knob where the bill meets the forehead unless you have a Chinese or African goose. Both breeds develop knobs as adolescents (usually no sooner than 4-5 months of age, sometimes later) that continue growing for around two years. Mixed geese may have a knob, but these are usually small in size.
Breeds with a knob: African (the knob is always black, although there is a White and Buff strain with orange bills - both extremely rare), Chinese (a black knob in one color, an orange knob when the goose is white).
Throat: The typical goose has a "clean" throat, where there is a curve from the base of the bill down the neck in a graceful arch. Three specific breeds develop a well defined loose flap of skin that dangles below the chin called a dewlap. Most hatchery stock will have a small dewlap that will take around a year to develop.
Breeds with a dewlap: The African - Exhibition and, to some degree, the Production - (a light grey-tan colored goose with a dark stripe down the neck), the Chinese (the same color as the African only very slender, also comes in white), and the Dewlap Toulouse (a large grey goose with a sagging belly).
Tuft: There is a single breed that is officially recognized with a tuft of feathers sticking out of its head. The Tufted Roman, a snow white, smaller breed is fairly uncommon. Recently a batch of meat geese were imported from France and a few of the Toulouse had a small tuft. These have been isolated and are being called Tufted Toulouse. Lastly, a breeder from the Ozarks was working on a Tufted American Buff. Tufted Buffs can be found occasionally.
Feathers
There is one breed with feathers that are unique to it alone. The Sebastopol (roughly pronounced as if saying "Constantinopol") has been bred to have long feathers that twist and curl as they fall along the bird's sides. The Sebastopol can have a smooth breast of average feathers, or be completely frizzled from neck to tail. This is a recessive gene, but it can crop up in mixed breeds. Most Sebastopols are white, with other colors being extremely hard to find.
Color
Unlike ducks and chickens, geese come in a fairly limited range of colors. So limited, in fact, they can be listed below without taking up too much space. Since the bird's coloring is key to it being of that breed, this is one of the rare times where it is fairly safe to use it as a means to judge what you have.
Brown: Found only in Africans and Chinese, the Brown coloring is a light grey-brown with a dark brown stripe running down the back of the neck. The underside is a lighter shade than the back, which tends to be fairly dark. The bill and feet are black. Since only two breeds are found in this color, any adult geese without a knob are mixes.
Buff: The buff is a dilution of the grey, and should be an even shade of fawn or tan with a white belly. Most commonly, any buff colored geese you find will be the American Buffs. However, this dilution is becoming popular in Sebastopols and Dewlap Toulouse (not Production/hatchery Toulouse).
Grey: The most common color is a slate grey with a white belly. This color is found in your Toulouse (Production and Dewlap) only. A lighter version of this coloring is found on the female Pilgrim, only white markings should be scattered around her face near the bill and around the eyes.
Saddleback: Saddlebacks can be buff or grey, where the head is a solid color, the neck is white, the back is colored, and the underside is white. The most common saddlebacks are Pomeranians, which are almost always grey, but are occasionally buff. A few small flocks of Sebastopols are also buff or grey saddlebacks.
White: White is on par with grey as the most common color geese are found in. The bird should be pure white throughout with an orange bill and feet. Most white geese are Embdens (which only come in white), White Chinese, and Sebastopols. Pilgrim ganders are white with grey markings on their back.
Size
Judging what you have based on size doesn't work very well with all of the hatchery stock geese on the market. Almost all Embdens from hatcheries are too small and the Romans, an extremely small breed, tends to be on par with the regular hatchery Toulouse.
While you can try to add that into your list to determine what you might have, it isn't recommended.