Learning to do a character analysis can certainly seem a bit overwhelming, but here are some things to look for that can make it easier. This formatting allows for limited space, so we shall only analyze Romeo with respect to a few tips, but below is also a link to an eNotes article that can further help with your analyses.
One thing to look for when doing a character analysis, which is analyzing an author's characterization, is whether or not the character behaves ethically. What are their moral decisions? When we first meet Romeo in Act 1, Scene 1, we see that we can actually question his moral decisions. Romeo is pining away, not just because he thinks he is in love with Rosaline, but because she refuses to sleep with him. We see this in the line, "she hath Dian's wit; and, in strong proof of chastity well arm'd, from love's weak childish bow she lives unharm'd." Diana is a goddess known for her chastity, therefore this line is stating that Rosaline is refusing to sleep with him. The reason Romeo has been out all night, nights in a row, is because he is pining and lusting under Rosaline's window, who is refusing him. In those days, intercourse outside of wedlock was sinful. Romeo's desires are even morally reproached by Friar Laurence in Act 2, Scene 3, when he proclaims, "God pardon sin! was thou with Rosaline?"
Another question to ask yourself is whether or not the character makes wise decisions. Since Romeo is heartbroken due to unreciprocated lust, it can be said that Romeo is equating love with lust, which may not be either entirely true, or entirely wise. As Friar Laurence points out, "young men's love then lies not truly in their hearts, but in their eyes," proving that Romeo is not a wise character. Romeo also makes the unwise decision of joining his friends in crashing the Capulet's ball. This decision ultimately leads to his demise, because it was for this decision that Tybalt attacked him and was killed, indirectly leading to Romeo's own death.
Another question to consider is: what are the things that are motivating the character? In Romeo's case, one thing that is motivating him to act upon lust and make foolish decisions is youth. Romeo is very young--either late teens or early twenties. As Friar Laurence points out, it is very characteristic of young men to unwisely act upon lust and make foolish decisions. But another motivation may simply be his stubborn, romantic, flighty nature. Romeo is not one that is easily counseled. We see Benvolio beg Romeo to listen to his advice in the first scene with the line, "Be rul'd by me: forget to think of her" and Mercutio says something similar in Act 1, Scene 4. We see that Romeo is a romantic in all of his long speeches that describe both Rosaline and Juliet, which are so full of allusions, figurative language, and rhetorical devices. His speeches stand in great contrast to Mercutio's, who is far more practical about love and dreams. We see Romeo being flighty when we see him being so very fickle. Therefore, both Romeo's youth and nature motivate his actions and are critical elements of his characterization.