Look for a didactic theme or moral tone in the work. Allegory is often used as an embodiment for moral qualities and messages as in Aesop's Fables. The story itself is constructed in such a way as to convey a central theme or lesson.
Take note of other literary devices such as satire that are often used in conjunction with allegory. George Orwell's political satire "Animal Farm," for example, uses animals and a farm setting as a representation of human society and a critique of politics.
Search for characters that are personifications of ideas like greed, envy or hate. Often their names help to decipher their literary purpose. John Bunyan's allegorical masterpiece, "Pilgrim's Progress," is a prime example with characters such as Christian, Old Honest and Lord Carnal Delight.
Identify fantasy, science fiction or supernatural elements in a work. These forms, both as a genre and a device, are often used metaphorically to reflect an idea or belief about the real world. C.S. Lewis in "The Chronicles of Narnia" uses fantasy as a genre and allegory as a literary device to do just that.