What is a summary of Chapter One or Part One of To Kill a Mockingbird?

Your initial question asked about an "Act One" of To Kill a Mockingbird.  There are no acts in the novel, although there is a Chapter One and a Part One.  Chapter One sets the stage for the novel, introducing the main characters of Jem, Scout, Dill, Atticus, and, of course, Boo Radley.  

Part One of the novel comprises the first 11 chapters.  Aside from initial introductions, this part goes in depth regarding the development of the novel's main characters.  Boo Radley is discussed repeatedly as the neighborhood "monster", but the mended pants and gifts in the tree suggest that perhaps we are not getting the full story.  Harper Lee, the author, introduces the trial of Tom Robinson and the town's reaction to Atticus' decision to take the case, in this part.  The actual trial, however, will serve as the focus in Part Two of the text.