It can be very difficult to know where to begin if you are not used to doing a character analysis, so I sympathise with you! There is good news, however. It does get easier the more you practise this skill. A character analysis normally refers to a couple of paragraphs where you describe the character, both refering to their physical appearance and their various traits and qualities as displayed in the text you are studying.
One way of doing this is, when you have finished the novel, brainstorm the character you are focusing on and identify his or her various traits. Are they active or passive? Are they good or bad? Are they intelligent or stupid? Starting off with such simple dichotomies should hopefully allow you to develop your character analysis to a more sophisticated level. Then, try and find some quotes from the novel to support your list of traits.
If you get stuck, try and find the passage where that character is first introduced and analyse it, thining about what is shows us about that character. Consider the character of Charles Darnay, and when he is introduced in Book the Second, Chapter Two:
The object of all this staring and blaring, was a young man of about five-and-twenty, well-grown and well-looking, with a sunburnt cheek and a dark eye. This condition was that of a young gentleman. He was plainly dressed in black, or very dark grey, and his hair, which was long and dark, was gathered in a ribbon at the back of his neck; more to be out of his way than for ornament. As an emotion of the mind will express itself through any covering of the body, so the paleness which his situation engendered came through the brown upon his cheek, showing the soul to be stronger than the sun. He was otherwise quite self-possessed, bowed to the Judge, and stood quiet.
What qualities stand out from this presentation? Hopefully you will have identified quickly the physical description, and moved beyond this to his traits and qualities. What is important is that his soul is described as being "stronger than the sun." The fact that he is "quiet self-possessed" in spite of being tried for treason says a lot about his character. Such strategies can help you as you develop your character analysis. I hope this helps. Good luck!
Characterization is accomplished in literature in two ways: directly and indirectly. Direct characterization is when the author simply provides direct description about a who a character is. A made-up example might be something like, "He was an ugly and evil villain who would stop at nothing to get revenge on his foes."
Most often, author's are not so obvious nor direct. Indirect characterization is used when characters are described through one of the following avenues: appearance, thoughts, actions, speech, and/or the reactions of others to them. Consider the first description of Miss Manette in chapter four (and remember, the reader is seeing her for the first time through Mr. Lorry's point of view):
...a young lady of not more than seventeen...a short, slight, pretty figure, a quantity of golden hair, a pair of blue eyes that met his own with an inquiring look, and a forehead with a signgular capacity...an expression that was not quite one of perplexity, or wonder, or alarm, or merely of a bright fixed attention, though it included all the four expressions...
In this very opening description the reader is given a full, but not complete, picture of Lucie Manette (Darnay). As her character unfolds throughout the story, she is revealed to be a passive character who, though somewhat frail and certainly not dominant, has such a capacity for affection that others are changed by her.
The process of characterization (or character analysis) begins with collecting evidence (in the form of quotes) of both direct and indirect characterization provided by the author. In addition to this, note any significant changes the character goes through in the course of the story. Once you have collected several pieces of evidence and noted change, you can use your own words to describe and ultimately define that character. A character who does not change is considered static while a dynamic character is one who does change. In your analysis, be sure to show evidence from the beginning, middle, and end of the text for completeness.