This novel basically charts the descent into savagery of a group of boys (some of them choir boys no less - an ironic touch) through their abandonment on an island with no adults.
The central opposition in the novel is that between the forces of civilisation and savagery, or order and chaos. Golding explores the competing instincts that dwell within us all: to live by rules, obey morals and act for the greater good of society, and then the opposite side, which is the desire to dominate, enforce one's will and act immediately to gratify desires.
This conflict is explored throughout the novel through examining the boys' gradual slide into lawlessness as they adapt to life in a barbaric jungle away from the normal controls on their behaviour (law, parents, school etc). These two forces are represented by the two characters Ralph (civilisation) and Jack (savagery).
Golding's conclusion is that the instinct for savagery wins out in the end. It is far more primal and fundamental to us than the instinct of civilisation, which he sees as a result of social conditioning rather than any moral goodness within humanity. We can see this through the example of the boys: when left to their own devices without any external forces of control, the instincts for savagery win out, even in the defender of civilisation, Ralph. The concept of the innate evil within all of us is central to understanding this novel, and is symbolised by the beast and the sow's head on the stake.
If you are after specific examples, you need to look at the gradual decline into savagery - how Jack and the hunters start painting their faces in Chapter 3 and how pig hunting becomes more important to them than the signal fire, then how all the boys, even Ralph, become intoxicated by their savage instincts hunting the pigs and join in the slaughter of Simon.