When you upload a sketch to the Arduino, any old sketch that was on there will be deleted. The first sketch given was just an example of an LED and button. Try uploading it and understanding how it works before asking more questions.
The second sketch is an extension that adds serial communication, so you can open your serial monitor (the little magnifying glass in the upper right hand corner) and see whether the button is pressed.
Your computer is receiving the serial messages, but using the Serial.read() sketch, your other Arduino can receive the serial messages too. You should try one Arduino at a time connected to the computer with both the write and read sketches before you combine them together.