What Do I Have?
Without a pedigree given to you with the rabbit, or at least viewed, it is virtually impossible to guarantee you have a purebred. Many backyard breeders cross individuals based on traits that they desire and not always will those breedings have parents of the same breed.
In addition, I have seen many people and pet stores selling rabbits as a particular breed that have been mistaken as to what they have. A lot of these are honest mistakes, with the pet stores purchasing "dwarf" rabbits from an individual who simply thinks that a Netherland Dwarf is a rabbit that is smaller than the giant meat breeds.
Because of all of this confusion, I have tried to break down the different ways to determine what type of rabbit you might have - or confirm that what you have isn't what you thought.
Understand that unless you are breeding for particular traits, the breed isn't entirely necessary. Just like dogs and cats, "mutt" rabbits make great pets. If your interests lie in breeding, you may want to start out with pure animals, then decide your focus from there. Mixed breeds cannot be shown and often sell for a fraction of the cost of purebreds - let alone for ones whose ancestry has been recorded.
Ears
One of the easiest ways to determine what you might have is to check the ears. If the ears flop over, you have one of the lop breeds. The current breeds with drooping ears are the American Fuzzy Lop (tiny with long fur), English Lop (large and long with ears that drag to the ground), French Lop (one of the giant breeds), Holland Lop (the smallest of the lops), Mini Lop (the most common in this category), and the Velveteen Lop (a new breed with short fur and a long, large body).
While pedigreed lops typically have babies that drop their ears by the age of eight weeks, it could take longer for other bloodlines. If you recently purchased a baby with ears that are partially drooping then give it time, they could still fall entirely. If they remain partially upright when the rabbit is 16 weeks or older then you have a mixed breed with some lop in the background.
Fur
Next is to look at the fur. There are five different types of fur, with all but one being unique to a single class or breed of rabbit.
Angora: This is the longest type of fur and has a soft, wool-like feel. Most rabbits with this type of fur were traditionally raised to spin wool, with the long strands harvested either by combing the rabbit out or by shearing it like a sheep. The long haired breeds are the American Fuzzy Lop (tiny with floppy ears), English Angora (with long fur on the ears and face), French Angora (with short fur on the ears and face), German Angora (a commercial wool producer), Giant Angora (the largest of this category), Jersey Wooly (a tiny breed), Lionhead (a tiny breed with long fur on the head and short fur on the body), and Satin Angora (with a satin sheen to the fur).
Normal: Most rabbits have short, smooth hair that feels a lot like stroking a cat (or in the case of a baby, stroking a kitten). Some colors have a glossy shine that may be mistaken for a Satin. Any breeds not listed in the other four categories fall under this one.
Rex: Rex fur is extremely short and dense, feeling a lot like crushed velvet. When you pet the rabbit from head to tail the fur will feel the same as if you stroke from tail to head. There are only three breeds with this type of fur: the Mini Rex (an extremely popular, small breed), the Rex (the larger version of the Mini), and the Velveteen Lop (a large breed with floppy ears).
Satin: When a Satin is held up next to another rabbit of the same color there is no mistaking it for anything else. Each hair is hollow, reflecting light differently and giving the coat a pearly sheen. Some colors may be more difficult to spot than others, such as the black Satin. There are only two breeds with this fur: the Mini Satin (a small, relatively rare breed), and the Satin (a large, popular breed).
Silver Fox: Of all the categories, this is the most difficult to stumble across. Only the Silver Fox breed has this type of fur, which is medium length and feels identical to an actual silver fox coat. The breed is critically rare and is traditionally black with silver frosting throughout. Breeders are working on chocolate and blue.
Body Type
Just like dogs, different breeds of rabbits have different shapes, with some being long and slender while others are short and squat. Unless you are extremely familiar with rabbits, this can be difficult for a person to break down. When determining the breed you might have, use this section sparingly. Some Holland Lops like to sit upright and, if they have poor conformation, may be mistaken for having a full-arched body, when in reality they are compact.
This information has been taken directly from the ARBA standards to keep from being muddled up by myself and is to help give you a guesstimation.
Full Arch: Rabbits will show an arch starting at the nape of the neck, running over the shoulders, mid-section, loin, and hips to the juncture of the tail. Most will show more depth than width.
The full arch breeds include: Belgian Hare, Britannia Petite, Checkered Giant, English Spot, and Rhinelander.
Semi-Arch: Rabbits carry good arch starting back at the shoulders and carrying through the base of the tail. Referred to as the mandolin type.
The semi-arch breeds include: American, Beveren, English Lop, Flesmish Giant, Giant Chinchilla, and Velveteen Lop.
Compact: Rabbits are lighter in weight and shorter in length than commercial breeds.
The compact breeds include: American Fuzzy Lop, Dutch, Dwarf Hotot, English Angora, Florida White, Holland Lop, Jersey Wooly, Lilac, Lionhead, Mini Lop, Mini Rex, Mini Satin, Netherland Dwarf, Polish, and Silver.
Commercial: Ideal meat rabbit. Rabbits are medium in length with depth equaling width, showing roundness of body and firmness of flesh.
The commercial breeds include: American Chinchilla, American Sable, Californian, Champagne d'Argent, Cinnamon, Créme d'Argent, French Angora, French Lop, Giant Angora, Harlequin, Hotot, New Zealand, Palomino, Rex, Satin, Satin Angora, Silver Fox, and Silver Martin.
Cylindrical: Rabbits are long, slim and cylindrical with fine bone and long slender head.
The cylindrical breed is the Himalayan.
Size
With most pet rabbits, smaller breeds are going to be larger than normal and giant breeds will be smaller, since most backyard breeders don't focus on keeping within size limits, preferring to focus more on color and personality. Because of this, use the following as a loose guide to determine what you might have.
Dwarf Breeds (1 3/4 to 3 1/2lbs): Britannia Petite, Dwarf Hotot, Jersey Wooly, Holland Lop, Netherland Dwarf, and Polish.
Small Breeds (2 1/2-5lbs): American Fuzzy Lop, Dutch, Himalayan, Lionhead, Mini Rex, Mini Satin.
Medium Breeds (4 1/2-7lbs): American Sable, Belgian Hare, English Angora, English Spot, Florida White, French Angora, Harlequin, Havana, Lilac, Mini Lop, Rhinelander, Satin Angora, Silver, Silver Martin, and Standard Chinchilla, Tan.
Large Breeds (8-12lbs): American, American Chinchilla, Beveren, Californian, Champagne d'Argent, Cinnamon, Crème d'Argent, English Lop, French Lop, Hotot, New Zealand, Palomino, Satin, and Silver Fox.
Giant Breeds (over 12lbs): Checkered Giant, Flemish Giant, Giant Angora, and Giant Chinchilla.
Color
Barring certain breeds, color is the least helpful way to determine the breed you have. Colors and patterns overlap in the different breeds, and mixed babies can stumble on having markings identical or similar to a particular breed without actually being one.
On top of that, many people work on developing new colors for breeds, making it difficult to keep up with what is a recognized color and what is a purebred variety a breeder is working on.
Some breeds, like the Californian, Hotot, and Dwarf Hotot, have very specific markings that identify what they are. These markings are also commonly found in commercial and dwarf crosses. Use the color guide sparingly and don't assume that just because your rabbit has a silver grey coat it is a Chinchilla, or that a white rabbit is a New Zealand.