Other examples of Atticus' influence over Jem and Scout in To Kill a Mockingbird:

• BOO RADLEY.  Atticus repeatedly scolds the children about their obsession with their neighbor, telling him to "stop tormenting that man." When he points out to Scout that it was probably Boo who placed the blanket upon her shoulders on the night of the fire, she begins to understand that Boo is not a threat to anyone.
• THE FINCH FAMILY.  Atticus is more realistic about his family history than his proud sister. The children come to understand that since the family has no real wealth, Aunt Alexandra only has her heritage on which to cling.
• RACIAL TOLERANCE.  Keeping Calpurnia as "a member of the family" is a daily reminder of Atticus' color blindness when it comes to black and white. He firmly cautions Scout to stop saying "nigger," because "it's common."

Mainly, Scout and Jem get influenced by their father through watching how he lives his life.  By watching how he acts, they learn important things about how he thinks people should act.

Two incidents that jump out at me:

• When Atticus kills the mad dog.  The two of them find out that their father thinks that you should not show off your skills just for the heck of it.  He also believes in being humble.
• When Atticus makes them go to Mrs. Dubose's house and read to her.  He is showing them there that you are supposed to love even those who hate you.