How does Golding show the beast?
Golding shows the beast in a figurative way and in a literal way. His belief, and the theme of the book, is that all mankind is flawed with a basic evilness that each person keeps in check, to one degree of success or another, only because society forces each person to do so. In the story, the boys are stripped of the society they knew and are put into a new world where they are free to create their own society. The society they create is evil and Golding contends that is what would happen without societal constraints. To show this inner evil, Golding used the personification of a beast.
First, the littlest boys are convinced there is a beast, they just don't know what it looks like or where it is. Some think it's in the water, some think it's among the creepers and vines and trees. When Sam and Eric see the dead parachutist from a great distance and think that what they see is something alive and moving, they are convinced that what they see is the beast. It is not quite human looking, but not too far removed from human in form. It is on top of the mountain as if it rules the area. It becomes the literal version of the beast.
When Jack hunts and kills the pig, then puts its head on the stake as an offering to the beast, the head, surrounded by flies, becomes the beast in a less concrete way. When Simon goes into his trance and "talks" with the head, which has become the Lord of the Flies, the source of the evil on the island is exposed. Simon had suspected that the source was inside of each of them, but the Lord of the Flies confirms that. The real beast, the figurative beast but the real evil, is what is inside of each person.