How does Katniss save her sister from the reaping?

Katniss saves Prim from the reaping by volunteering to go into the arena instead of her little sister.

Really, Katniss saves Prim from The Hunger Games, not the reaping. When Prim's name was called to come onto the stage so she would be announced as a tribute, Katniss was pulled back into memories. Katniss couldn't stand the thought of Prim going into the Hunger Games, she loved her so much. So Katniss volunteered to take Prim's place, and Prim was saved.