Miss Caroline Fisher is certainly a memorable minor character from the novel and one who is developed sufficiently for you to write a character sketch about her. In fiction writing, much as in life, characters reveal themselves primarily by what they say and do. Also, they are revealed by what others say about them and by what others think and feel about them.
In writing a character sketch of Miss Caroline, begin by making a list of what she says and what she does in the classroom in Chapter 2. Then, make another list of what Scout tells us about her and what Scout thinks and feels about her.
Once you have all your notes, you should be able to identify Miss Caroline's major character traits. For instance, she tries hard to entertain the children, but the story is boring to them because it is so far removed from their daily lives--at least to Scout. She disapproves of Scout's knowing how to read and tells her she can no longer read with Atticus at home because only she can teach Scout properly. Finally, by way of example, she tries to lend money to Walter Cunningham so that he will have something to eat for lunch. She does not realize why he won't accept it.
When you "add up" these examples of what Miss Caroline says and does, you can conclude that she is a sincere teacher, but one who is inexperienced and unfamiliar with the lives of her students. Finding other examples of what she says and does will reveal more about her, as well. Also, your notes about what Scout tells us directly about Miss Caroline and how Scout feels about her will further reveal her character. Writing a good character sketch begins with researching what the character says and does and what others say and feel about him or her. Good luck!