The ways in which an author, such as Shakespeare, presents characters actually refers to characterization. Characterization is a term we use to describe how an author presents a character as a person through their character traits, or personality traits. There are many different things one can look at to analyze characterization. A few things to consider are, what does the character say; what does the character do; what are the character's driving motives; what kind of decisions does the character make, good or bad; how do other characters respond to the character in question; do the other characters like him or her, why or why not? Since we are limited to space, below are a few things to help get you started.
Romeo is a good character to analyze for characterization and the very first scene is a good place to start. What can we learn about him through his conversation with Benvolio? What can we make of Romeo's reaction to being rejected by Rosaline? Is it rational or irrational? Does his love for Rosaline seem mature and sincere, or young and insincere?
When we first meet Romeo, we know that he is extremely depressed because he is being rejected by Rosaline. He is so heartbroken about it that his father says Romeo has been seen night after night crying under a certain grove of trees in a certain part of town, presumably the part of town where Rosaline lives. In fact, in Romeo's first long speech, he feels so hurt by love that he describes love as a torturous, contradictory emotion, as we see in his lines:
O brawling love! O loving hate!
Misshapen chaos of well-seeming forms!
Feather of lead, bright smoke, cold fire, sick health! (I.i.174-178)
However, even his cousin Benvolio feels that Romeo is letting his emotions run away with him, that he is taking things too far. We see that Benvolio thinks Romeo is acting irrationally when Benvolio begs Romeo to take his advice and stop thinking of Rosaline. But, Romeo's only stubborn response is that he can't possibly learn how to stop thinking.
From this one little scene, we are able to deduce that Romeo is the type of person who is emotionally driven; he allows his emotions to govern him rather than his own sense. We can further deduce that Romeo's love for Rosaline is actually irrational and very immature. Furthermore, Romeo's refusal to listen to Benvolio's advice shows that he is very young and stubborn. Therefore, we see that Shakespeare presents Romeo as a very irrational, emotionally driven, and stubborn youth.