Irving offers several clues in his description of the man in the forest so that Tom and readers know that he is the devil.
1. The man seemingly lives in the forest when Tom meets him. Puritans from the story's setting believed that the devil roamed the woods around their communities, waiting to tempt humans into signing his black book. The devil even ask Tom what he is doing on "his grounds," revealing that the dark forest is his domain.
2. He is called "the black man," but Irving is not describing his race with that description. He goes on to write:
"His face was neither black nor copper colour, but swarthy and dingy and begrimed with soot."
The soot suggests that this creature spends most of his time near fire (hell-fire).
3. When the devil and Tom are finished talking, he presses his thumb against Tom's forehead, and Tom cannot remove the black, sooty mark when he gets home.
4. Finally, the devil is in the process of burning trees (which represent people's souls) when Tom comes upon him. Only a supernatural creature like the devil would have such power.
Tom Walker recognizes this man as the devil because the man makes a number of allusions which Tom understands. The man says that in some countries, he is known as a "wild huntsman" or a "black miner," for example, and that "red men" make human sacrifices in his honor. Moreover, he also claims to be present at the "persecutions of Quakers and Anabaptists," as well as being a "patron" of people who procure and sell slaves and the "grand master" of the witches in Salem.
When the devil tells Tom of these various identities, Tom instantly recognizes his true identity. Tom, therefore, is familiar with both historical and contemporary folklore, enough to understand that this man is the devil and cannot be any other figure.
Later in the text, Tom's belief in the devil's identity is further reinforced when he notices that the black fingerprint, used by the devil as his signature, is burnt onto his forehead and cannot be removed, no matter what he does.