There are two characters: the Narrator and the Old Man.
The Narrator has clearly descended into madness. As for the "literal" characteristics, if you mean physically, we do not know what the Narrator looks like. He tells the story in first person and does not describe his own looks. One can describe his voice, however, as being full of panic, fear, and apprehension. As his madness increases, so too does his desire to rid himself of the Old Man with whom he lives. He is convinced that the man's eye is evil and that he wishes to do the Narrator harm.
As to the Old Man, we have more knowledge of him physically and less psychologically. He has blue eyes, one of which is cloudy (probably due to cataracts) and their odd appearance makes the Narrator think he possesses some sort of evil intent. He is frail, sleeps a lot and deeply. He is appears to be wealthy, due to the Narrators descriptions of his "gold" and "treasures." The Old Man is probably completely unaware of the Narrator's burgeoning hatred.