The idea of the story, A Sound of Thunder, is that changing even a small thing in the past can make drastic changes in the future. The main character is going on a dangerous safari and learns the rules from the start.
Climax
A man named Eckles is going to travel back in time with some other men for a safari. Before they leave they are given the rules, and then he reads a sign by the desk. Eckles mentions how happy he is that Keith won the presidential election rather than Duetscher.
Falling Action
The men travel back in time. They are told not to walk off a path, so they don't change anything in the future. When the T-Rex they are planning on killing walks by, Eckles gets scared and walks off the path. The safari guide, Travis, is very angry with Eckles and threatens to leave him behind.
Resolution
Upon returning, the men from the safari realize that the office seems a little different, including the sign Eckles had read before they time-traveled. Eckles then looks through the mud on his boots and sees he stepped on a butterfly.
Eckles asks who won the presidential election and finds out it was Duetscher. The man they believed would be more of a dictator than a president.
Eckles begs to go back and save the butterfly, but it is too late. Travis kills Eckles for walking off the path and changing the future.