One of the best ways to know you're reading a Poe poem is to look for spooky, scary, melancholy imagery. Poe is one of the first American masters of horror, and almost all his work deals with fear, danger, monsters, terror, depression, and death – sometimes all at the same time. Fun stuff, huh?
Another Poe calling card is the way he plays with language. He loves to try out the craziest words he can find – you're probably not going to hear a lot of other people use the word "tintinnabulation" in normal conversation. He's a wizard with other poetic sound effects too, like repetition, alliteration, and onomatopoeia. So, if you're reading a spooky poem full of unusual sounds and words, chances are you're dealing with Edgar Allan Poe.