I am having trouble finding direct characterization examples and indirect characterization examples for Arthur Dimmesdale in The Scarlet Letter.
The introduction of Reverend Arthur Dimmesdale into the story of The Scarlet Letter comes through an indirect characterization as well as a direct characterization. Characterization reveals the traits, values, beliefs, appearance, etc. of a character. Indirect characterization reveals these things through dialogue or actions or reactions to events or other characters. Direct characterization reveals these things through a narrator who states directly that a character has specific traits, beliefs, etc.
When Reverend Wilson--the "eldest clergyman of Boston," is speaking to Hester in Chapter 3--makes references to Dimmesdale, these references tell readers that Dimmesdale had been Hester's clergyman, for she attended his church; is godly; is a youth; is well acquainted with Hester and knows her "natural temper"; has the strength of his convictions to oppose the eldest clergyman who is undoubtedly his superior and supervisor; has a "young man's over-softness" of heart.
All these revelations of Dimmesdale's character are made through indirect characterization: the reader learns these traits through dialogue that exposes another character's understanding of Dimmesdale. As an aside, with indirect characterization, it is important to know whether the source speaking, in this case Reverend Wilson, is a reliable character who is trustworthy or an unreliable character who view may not be trustworthy.
Two paragraphs later the narrator reveals more things about Dimmesdale. The narrator revealed that Dimmesdale came from "one of the greatest universities in England"; he has "eloquence and fervor"; he is already rising to "eminence" (recognition in his work); has a high white brow and brown "melancholy eyes," etc.; has self-restraint (ironically noted). All these revelations are made through direct characterization wherein the narrator knows information about Dimmesdale and imparts at least some of what he knows to the reader directly. As an aside, with a third person omniscient narrator, the narrator is assumed to be trustworthy--but be on guard when studying contemporary literature.