Please help me with an introduction and thesis statement for an essay explaining the ways in which an author's background influences the depiction of her characters.
An essay in which you discuss how an author's background influences the depiction of her characters is a form of what literary scholars call "biographical criticism." One of the first steps in thinking about developing a thesis statement for this sort of essay is researching the author to discover whether the characters are similar to ones with which the author was really acquainted or ones very distant from the author's own personal circle. For example, Jane Austen and George Eliot write about characters very similar to their own social circle, with certain characters in Eliot's work probably being thinly disguised versions of actual people she knew, while other authors, such as Anne Radcliffe or J.K.Rowling, write about exotic or unreal worlds.
If you think that a work is a thinly disguised story about actual people in the authors's life, a genre technically known as a "roman a clef", your thesis statement should provide evidence for that. For example, if you were writing about Margaret Laurence, you could begin with the thesis "Laurence considered The Diviners her spiritual autobiography, portraying her coming of age as a writer," and your introductory paragraphs should cite interviews in which Laurence explicitly states that she considers the work autobiographical. If writing about Jane Eyre, a possible thesis would be "Jane Eyre reflects Charlotte Brontë's experience working as a governess in 1839 and 1841." Similarly, the introductory paragraph should cover the relevant biographical details and how they are similar to elements of the novel.
Even in an unrealistic novel, the author's background might explain certain aspects of the characters. For example, an author who was bullied as a child might write especially sympathetically about bullied children, or an author who is deeply religious might explore moral dilemmas from a theological perspective. In all cases, a thesis statement needs to make a clear and succinct claim about the precise elements of an author's background that affect portrayal of a specific character and the introduction needs to expand upon that thesis and point forward to how you will support the thesis.