What are some examples from the text of the boys being affected/changed because of the beast being on the island?

There are at least three beasts that are "on the island" in Lord of the Flies, and each has effects on the boys. The first, the "beast from water," is an imaginary beast that represents the boys' nameless fears. This beast affects the boys in at least two ways. First, the littluns consistently have nightmares and cry during the night. Considering that they have been separated from their homes and families and have endured a traumatic plane crash, this is not surprising. But rather than speaking about what is really bothering them, they imagine a beast. Ralph tries to address the issue and convince the boys their fears are groundless, but during the evening meeting the boys start to get spooked. Jack plays on their fears and leads them onto the beach in defiance of the rules. Ralph fears the boys have become "animals." 

The second beast is the "beast from air," a fallen paratrooper who lands on the island during the night. Samneric discover it, but are too panicked to investigate. They run frightened back to the other boys. Because this beast is on the mountain where the signal fire was, Ralph feels they are beaten and will never be rescued. However, Piggy uses surprising "intellectual daring" and suggests moving the signal fire to the beach. Simon, however, is determined to investigate the beast and climbs alone to the mountain and discovers the truth about it; he returns to the camp with the intention of letting the boys know the good news that the beast is nothing to fear, but they kill him before he can explain.

Finally, the third beast is the Lord of the Flies that Simon sees in his vision. This beast affects Simon by confirming to him that he was right about the beast--it is really "mankind's essential illness," the tendency toward evil that resides inside every person. Unfortunately Simon is unable to share his insights with the other boys; first they mock him when he suggests "maybe it's only us," and then, when he appears at the feast, they murder him, proving that they have succumbed to the very beast Simon tried to warn them about.