Brown rats ("Rattus norvegicus") are also known as Norwegian rats, Norway rats, gray rats, sewer rats or wharf rats. Brown rats can range in color from black to brown to white. This species of rat is the one that produced today's stock of domesticated pet rats. This article is about how to identify wild brown rats, not their domesticated cousins.
Look at the length of the tail. If the tail is shorter than the length of the body (including the head) the rat is likely a brown rat. (In contrast, the black rat's tail is longer than its body.) This is the best way to identify a brown rat.
Look at the ears. A brown rat has very fine hair on its ears. (Warming: Never catch a wild rat in order to examine its ears!)
Look at the nose. Brown rats have more blunt noses, in contrast to black rats which have more pointed noses.
Look at the overall body shape. Brown rats tend to have a rounder body shape than black rats.
Consider the environment in which is it living. Is the rat in a warm or cold climate? Brown rats are usually found in temperate or colder climates, such as North American, Europe, or northern Asia. Their cousins, the black rats, are more likely to be found in tropical or subtropical climates, closer to the equator. (This was not always the case. During the Middle Ages, the black rat dominated Europe, but when the brown rats came in, the blacks rats moved south and have stayed there ever since.)
Watch its behavior. When it flees, does it try to go down or into something, or is its first instinct to go upward? Brown rats are more inclined to run along the ground or try to disappear down a hole (in contrast to black rats who tend to flee upwards). Brown rat do climb, however, so this method of identification is not fool-proof.