In To Kill a Mockingbird, how did the Finches originally come to Maycomb?
The answer can be found in the first chapter of the book. There, Scout goes into the family history a little. The family has been living in the county ever since their first ancestor to come to America set up a plantation at "Finch's Landing." Ever since then, we are told, the Finch men would live at the Landing and raise cotton. So the family has been in Maycomb County ever since Simon Finch (the ancestor) set up his plantation there.
Atticus becomes the first that we know of to break with that tradition. After studying law in Montgomery, he comes to the town of Maycomb to set up his legal practice. That is how the Finch family comes to be in the town of Maycomb.