When writing about a character's traits and personality you want to give a well-rounded overview. In order to do so, it is important to look at a variety of aspects. A great method I teach my students is STEAL:
- SPEECH: What does the character say? How do they speak?
- THOUGHTS: What is revealed through the characters thoughts and feelings (usually established through first-person narration)?
- EFFECTS ON OTHERS: How do other characters feel, behave, or react to this character?
- ACTIONS: What does the character do? How does the character behave?
- LOOKS: What does the character look like? How does he or she dress?
The important thing to remember is that as you approach each of these points you should be careful to attribute meaning for each example. For instance, when we study Brave New World we use this method to characterize Bernard Marx. When Bernard tries to disassociate himself with the Savage and Hemholtz during the riot for soma, he is displaying cowardice. I really push my students to attribute a specific trait/adjective to the examples they cite.
Hope this helps. Also, I don't take any credit for this method; it was passed on to me from another teacher. A quick google search for "characterization STEAL" will turn up further information about this method.
A common problem in student essays about character is that emphasis is placed not on what characters are like but rather on what they do. Therefore, the most significant element, no matter what approach you use or might select is that actions, comments, and speeches from the story should be introduced only to reveal qualities of the character being studied. The story materials should never become an end in themselves, never a retelling of the story. Try to focus on their dialogue and what is says and what it doesn't say about them. Also, focus on not only what they think but how others feel about them.
My answer will be a bit long. :D
When writing about a character, you must take every part of them into consideration. How do they react the world around them: both natural and material. What do they like, hate, love, or feel neutral about? How does their ethnicity, religion, political views, etc. change their outlook on life? Are they serious or carefree? What do they look like; are they intelligent; are they street smart? How do these things add up to their actions, thoughts, and inner psyche? How to other characters, readers, and writers view these characters?
Most importantly: how does the character move the plot forward, change the plot, and/or handle the actions of the story.
Describing a character ultimately stems from your own perception of them. What one person may see as a strong and lovable character, another may see as being weak and boring. Your opinion matters, but it is also vital to try and scope out the writer's original intention. Often this may conflict with your own theory, and that is when you must decide whether or not to embrace the author's point of view or stick to your original idea.
For example (and this is my inner nerd coming out ;)), in Harry Potter, I LOVE Severus Snape. I see him as flawed but deeply beautiful: a man as gentle as he is rough. J. K.Rowling says that, for all his atonement and love for Lily, he is basically not a nice guy: even though he is one of her favorite characters. Now, I choose to stick to my interpretation of Severus, even though it conflicts with the author's intent. That is the kind of thing that will be up to you. Generally, I think that author intent is vital, but there are times when one cannot help but see things entirely different!
Another example: Some people, even scholars, do not read the sections of Dante's Vita Nuova that do not include Beatrice. They feel that those sections sully the romance and passion of the treatise. I feel that it's important to read the entire work. It is not a work of fiction, and why ignore the facts? This is rather ignorant. I may not like the fact that Dante wrote about women who were not Beatrice, but it doesn't change history.
Overall, be critical and open-minded when writing about a character. Pay close attention to details. Write with honesty and integrity to your opinion. Literature is often oh-so-subjective. Find your view and make a case for it. You can't go wrong when you write about a character unless you don't take the time to analyze them.
Good luck, and I hope this helps!