In Lord of the Flies what are the main conflicts and how do they progress, how do the characters deal with them and what is the outcome?It is for...

This is obviously a loaded question--one that can only be
responded to in a detailed essay.  (And I'm assuming that's what your assignment
requires.)  Here are some points to consider that might help you plan your
response:

William Golding wrote this novel to examine human
nature and how stressful situations affect people's actions.  The primary conflict
present in Lord of the Flies actually centers around the boys'
struggles against themselves; this is evidenced by the fact that Simon, after his
encounter with the lord of the flies, tries to report to the others that there is no
beast--that the beast they're fighting against is actually within
them. 

Different characters respond to the stresses of life
on the island differently.  Ralph is the boy who longs for order, and he tries to
establish (and enforce) rules.  Jack, on the other hand, promotes savage behavior
through his insistence that the children hunt regularly--even when it's clear the boys
are hunting for sport rather than for food.  Piggy is the voice of reason, but he is
powerless without Ralph.  Simon, the purest child on the island, is able to resist the
temptation to resort to savage behavior when the others are
not. 

Eventually, chaos reigns on the island, and boys die
as a result.  Simon is killed because he is mistaken for the beast, and with him dies
the information that could save the rest of the children on the
island. 

Obviously, there are many other conflicts in the
novel, but they all stem from this main idea. 

I hope this
was helpful.  Good luck with your essay!