How does Atticus seek to instill conscience in his children in To Kill a Mockingbird?
Atticus is a believer in modeling the behaviors, like having an active conscience, that he would like to see in others, especially his children. He rarely relies on didactic measures, ones that teach a moral lesson in an obvious way, preferring instead to live as he wishes to see his children live. For example, when Atticus is called upon to shoot Tim Johnson, a dangerously rabid dog, his children learn some very important lessons.
First of all, they learn from their father that sometimes, you have to do things you don't want to do for the sake of other people. Atticus is conscience-stricken and clearly reluctant to shoot the dog, and he does so only at the insistence of Heck Tate, who practically forces the rifle into his hands. But Atticus follows through, knowing that he is saving the lives of the people who live nearby and putting the poor dog out of his rabid misery.
Secondly, when Miss Maudie tells Jem and Scout about their father's reputation as 'Ol One-Shot,' they learn that their father is not only a well-respected and talented shooter, he is a humble one who has never once bragged about his skills. Atticus's humility also earns him the respect of his community. Even Jem recognizes at this moment that Atticus has a conscience like a "gentleman" and expresses his pride in his father by stating he (Jem) is a gentleman too, just like Atticus.
Atticus teaches his children about the importance of being tolerant of the actions and words of others. When Scout has problems with her teacher and Walter Cunningham on the first day of school, Atticus presents his daughter with his endearing words of wisdom about climbing into another person's skin in order to understand things from their point of view. Atticus teaches Jem and Scout to never take the life of an innocent being--it being "a sin to kill a mockingbird." He teaches the children to respect all people--black or white--and how it is far worse to take advantage of a black man than a white man. He teaches Jem that there are many types of courage (Mrs. Dubose), and that people never brag about their talents (Atticus' marksmanship). He teaches Scout that fisticuffs is no way to settle an argument, and he shows Jem that a person must pay for his acts of violence (Mrs. Dubose). He teaches them that people are not always what they seem (Boo Radley), and that even if they are, they deserve respect (Aunt Alexandra).