Melissa Gilbert played the role of Laura Ingalls Wilder for the entire series.
Alison Arngrim played the role of Nellie Oleson, the mischievous and often disliked antagonist of the show.
There was some confusion in the early seasons because Melissa Gilbert was very young and the producers wanted to avoid the fatigue of long filming hours for the young actress. They used two sets of identical twins (Alison and Melissa, and another pair whose names have faded from public memory) to play the role of Laura. But as Melissa Gilbert aged, she took over the role permanently.
Both Melissa Gilbert and Alison Arngrim have had successful careers in entertainment, though Alison's path has been more marked by comedic roles, including her memorable turn as the character "Nellie Oleson" in "Little House on the Prairie".
If you have any more questions about the show, feel free to ask!