This has been a problem for many readers and critics. The exact circumstances aren't very plausible. The boys are being evacuated because there's a war going on, and their plane is attacked. But how could the entire plane just disappear? How do the boys get off a burning plane without parachutes or something? Why are there no dead or wounded? It's all pretty far-fetched.
The answer is that you mustn't take the situation literally. Golding is writing a fable, and as such he is at liberty to tweak reality as much as necessary to get his theme across. The important thing to remember is not how they got there, but that the fact that the boys are safe, with all their physical needs provided-for, removed from the violence of war, and free to let their natural, child-like goodness and innocence to blossom.
After having to be evacuated from where they were, the plane the boys were on was most likely hit by lightening. Piggy thinks they were shot down, mostly because the pilot made comment about the airport they had just left being bombed. In the first chapter, however, Ralph makes reference to a storm and it is more likely that the plane was hit by lightening in the storm. After the crash landing the plane went off the far side of the island and sank with the pilot and some of the boys still on it.
During a future atomic war, the plane the boys are in is shot down over the island upon which they become marooned.
The details are in the very beginning of the first chapter. Here is a brief excerpt:
"We was attacked!"
"When we was coming down I looked through one of them windows. I saw the other part of the plane. There were flames coming out of it."
They were being evacuated via airplane because of an atomic bomb threat (a threat that they found out was real once they were in the air). During that evacuation, their plane was shot down and they landed on the island.