When one looks for the personality traits of a character, one is really analyzing how the author characterizes the character. Characterization is the image of the character the author creates for the reader. We can also refer to personality traits by the term character traits. Character traits would be things like loyalty, ambitiousness, rebelliousness, anything that identifies the character as a whole. We analyze the author's characterization of a character to determine the personality traits, or character traits. Things we can analyze to determine these traits are what the character says; does; thinks; feels; what their actions are, but more importantly, what their driving motives are; and also, how other characters respond to the character you are analyzing.
One good character to analyze for personality traits is Hermia. We learn a great deal about her personality in the opening scene. In fact, her first line is boldly addressed to Duke Theseus in defense of her perspective on Lysander. When Theseus argues in defense of her father's view of Demetrius, saying that he is a "worthy gentleman," Hermia boldly claims, "So is Lysander" (I.i.53-54). Hermia's boldness shows us that she is no shrinking violet. She is bold, assertive, and values her own opinion. We see further evidence of how much she values her own opinion when we see her crying to Lysander about the injustice of being forced to allow someone to choose the one to love for her, as we see in her line, "Oh hell! to choose love by another's eyes" (141). Hence, we see through even this one scene that some of her personality traits are boldness, assertiveness, and independence.
Hence, we see that by dissecting the things the character does, says, and thinks, we can determine personality traits, or character traits.